Load
Estimation
Plot
linear-demand linear-cost, \(\sigma = 1\)
\(\theta =
0.05\)
\(\alpha_2 =
0.1\)
\(n = 50\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.817
|
1.000
|
7.959
|
9.580
|
15.288
|
|
|
alpha1_hat
|
100
|
0
|
0.825
|
0.857
|
−1.470
|
0.766
|
3.413
|
|
|
alpha2_hat
|
100
|
0
|
0.110
|
0.081
|
−0.105
|
0.109
|
0.348
|
|
|
alpha3_hat
|
100
|
0
|
0.979
|
0.217
|
0.494
|
0.962
|
1.691
|
|
|
gamma0_hat
|
100
|
0
|
0.885
|
2.320
|
−17.279
|
1.197
|
4.363
|
|
|
gamma1_hat
|
100
|
0
|
2.497
|
9.899
|
−12.773
|
1.136
|
70.757
|
|
|
gamma2_hat
|
100
|
0
|
1.011
|
0.233
|
0.530
|
0.988
|
2.311
|
|
|
gamma3_hat
|
100
|
0
|
1.030
|
0.317
|
0.651
|
0.997
|
3.438
|
|
|
theta_hat
|
100
|
0
|
−0.808
|
5.535
|
−41.122
|
−0.060
|
9.001
|
|
|
theta_hat_t_stats
|
100
|
0
|
−0.107
|
1.107
|
−3.315
|
−0.044
|
2.587
|
|
|
R2_demand
|
100
|
0
|
0.370
|
0.292
|
−1.623
|
0.433
|
0.715
|
|
|
R2_supply
|
100
|
0
|
0.276
|
0.775
|
−6.837
|
0.411
|
0.734
|
|
\(n = 100\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.978
|
0.748
|
8.375
|
9.847
|
12.592
|
|
|
alpha1_hat
|
100
|
0
|
0.829
|
0.670
|
−0.830
|
0.745
|
2.707
|
|
|
alpha2_hat
|
100
|
0
|
0.116
|
0.061
|
−0.056
|
0.113
|
0.304
|
|
|
alpha3_hat
|
100
|
0
|
0.999
|
0.167
|
0.570
|
0.990
|
1.613
|
|
|
gamma0_hat
|
100
|
0
|
0.845
|
1.132
|
−2.634
|
0.791
|
2.968
|
|
|
gamma1_hat
|
100
|
0
|
0.865
|
1.887
|
−8.034
|
1.090
|
4.744
|
|
|
gamma2_hat
|
100
|
0
|
1.017
|
0.171
|
0.664
|
1.012
|
1.493
|
|
|
gamma3_hat
|
100
|
0
|
1.018
|
0.162
|
0.711
|
0.988
|
1.407
|
|
|
theta_hat
|
100
|
0
|
0.147
|
0.959
|
−2.028
|
0.059
|
4.702
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.081
|
0.930
|
−1.825
|
0.123
|
2.907
|
|
|
R2_demand
|
100
|
0
|
0.325
|
0.241
|
−0.787
|
0.387
|
0.644
|
|
|
R2_supply
|
100
|
0
|
0.305
|
0.176
|
−0.385
|
0.332
|
0.544
|
|
\(n = 200\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.973
|
0.410
|
9.143
|
9.948
|
10.873
|
|
|
alpha1_hat
|
100
|
0
|
0.947
|
0.358
|
0.030
|
0.932
|
1.842
|
|
|
alpha2_hat
|
100
|
0
|
0.104
|
0.034
|
0.028
|
0.103
|
0.204
|
|
|
alpha3_hat
|
100
|
0
|
0.998
|
0.103
|
0.757
|
0.985
|
1.293
|
|
|
gamma0_hat
|
100
|
0
|
0.853
|
0.751
|
−0.897
|
0.999
|
2.610
|
|
|
gamma1_hat
|
100
|
0
|
1.016
|
0.984
|
−3.260
|
0.931
|
3.577
|
|
|
gamma2_hat
|
100
|
0
|
1.011
|
0.107
|
0.780
|
1.008
|
1.251
|
|
|
gamma3_hat
|
100
|
0
|
1.021
|
0.103
|
0.828
|
1.003
|
1.332
|
|
|
theta_hat
|
100
|
0
|
0.067
|
0.499
|
−1.557
|
0.102
|
2.117
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.162
|
1.034
|
−2.557
|
0.317
|
2.408
|
|
|
R2_demand
|
100
|
0
|
0.332
|
0.127
|
−0.047
|
0.341
|
0.540
|
|
|
R2_supply
|
100
|
0
|
0.308
|
0.134
|
−0.184
|
0.324
|
0.572
|
|
\(n = 1000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.997
|
0.199
|
9.646
|
9.993
|
10.439
|
|
|
alpha1_hat
|
100
|
0
|
0.995
|
0.169
|
0.621
|
0.983
|
1.359
|
|
|
alpha2_hat
|
100
|
0
|
0.101
|
0.018
|
0.067
|
0.101
|
0.140
|
|
|
alpha3_hat
|
100
|
0
|
1.001
|
0.046
|
0.901
|
0.994
|
1.106
|
|
|
gamma0_hat
|
100
|
0
|
0.980
|
0.319
|
0.045
|
1.018
|
1.729
|
|
|
gamma1_hat
|
100
|
0
|
1.032
|
0.315
|
0.194
|
1.014
|
1.988
|
|
|
gamma2_hat
|
100
|
0
|
1.003
|
0.051
|
0.889
|
0.997
|
1.152
|
|
|
gamma3_hat
|
100
|
0
|
1.003
|
0.042
|
0.875
|
1.003
|
1.110
|
|
|
theta_hat
|
100
|
0
|
0.037
|
0.165
|
−0.484
|
0.047
|
0.487
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.202
|
0.947
|
−2.282
|
0.293
|
2.470
|
|
|
R2_demand
|
100
|
0
|
0.342
|
0.050
|
0.237
|
0.340
|
0.458
|
|
|
R2_supply
|
100
|
0
|
0.336
|
0.053
|
0.213
|
0.336
|
0.456
|
|
\(n = 2000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.996
|
0.146
|
9.640
|
9.993
|
10.428
|
|
|
alpha1_hat
|
100
|
0
|
1.012
|
0.118
|
0.683
|
1.016
|
1.274
|
|
|
alpha2_hat
|
100
|
0
|
0.099
|
0.011
|
0.073
|
0.099
|
0.124
|
|
|
alpha3_hat
|
100
|
0
|
1.000
|
0.037
|
0.909
|
1.002
|
1.081
|
|
|
gamma0_hat
|
100
|
0
|
1.037
|
0.203
|
0.572
|
1.049
|
1.469
|
|
|
gamma1_hat
|
100
|
0
|
0.997
|
0.244
|
0.376
|
1.000
|
1.534
|
|
|
gamma2_hat
|
100
|
0
|
0.996
|
0.031
|
0.926
|
0.994
|
1.078
|
|
|
gamma3_hat
|
100
|
0
|
1.000
|
0.026
|
0.931
|
1.000
|
1.060
|
|
|
theta_hat
|
100
|
0
|
0.046
|
0.130
|
−0.225
|
0.042
|
0.325
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.384
|
1.082
|
−2.184
|
0.370
|
2.702
|
|
|
R2_demand
|
100
|
0
|
0.332
|
0.041
|
0.221
|
0.332
|
0.431
|
|
|
R2_supply
|
100
|
0
|
0.338
|
0.034
|
0.261
|
0.341
|
0.414
|
|
\(\alpha_2 =
0.5\)
\(n = 50\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.059
|
1.165
|
7.650
|
9.738
|
14.910
|
|
|
alpha1_hat
|
100
|
0
|
1.176
|
1.935
|
−3.982
|
1.278
|
7.462
|
|
|
alpha2_hat
|
100
|
0
|
0.490
|
0.207
|
0.124
|
0.465
|
1.534
|
|
|
alpha3_hat
|
100
|
0
|
0.985
|
0.246
|
0.477
|
0.942
|
1.737
|
|
|
gamma0_hat
|
100
|
0
|
0.729
|
1.769
|
−8.802
|
0.906
|
3.573
|
|
|
gamma1_hat
|
100
|
0
|
0.810
|
3.272
|
−5.914
|
0.868
|
15.210
|
|
|
gamma2_hat
|
100
|
0
|
1.029
|
0.261
|
0.555
|
1.012
|
2.072
|
|
|
gamma3_hat
|
100
|
0
|
1.049
|
0.268
|
0.410
|
0.999
|
2.476
|
|
|
theta_hat
|
100
|
0
|
0.129
|
0.535
|
−1.646
|
0.127
|
1.327
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.167
|
1.045
|
−3.056
|
0.318
|
2.177
|
|
|
R2_demand
|
100
|
0
|
0.458
|
0.301
|
−1.023
|
0.537
|
0.783
|
|
|
R2_supply
|
100
|
0
|
0.493
|
0.224
|
−0.832
|
0.528
|
0.854
|
|
\(n = 100\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.954
|
0.651
|
8.636
|
9.896
|
11.753
|
|
|
alpha1_hat
|
100
|
0
|
1.072
|
1.230
|
−1.860
|
1.047
|
3.562
|
|
|
alpha2_hat
|
100
|
0
|
0.486
|
0.131
|
0.170
|
0.479
|
0.855
|
|
|
alpha3_hat
|
100
|
0
|
1.000
|
0.157
|
0.639
|
0.996
|
1.408
|
|
|
gamma0_hat
|
100
|
0
|
0.845
|
0.956
|
−1.477
|
0.926
|
2.493
|
|
|
gamma1_hat
|
100
|
0
|
0.945
|
1.557
|
−2.514
|
0.754
|
6.600
|
|
|
gamma2_hat
|
100
|
0
|
1.022
|
0.139
|
0.782
|
1.020
|
1.473
|
|
|
gamma3_hat
|
100
|
0
|
1.019
|
0.148
|
0.639
|
1.030
|
1.404
|
|
|
theta_hat
|
100
|
0
|
0.080
|
0.275
|
−1.013
|
0.106
|
0.552
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.202
|
0.932
|
−2.695
|
0.400
|
2.030
|
|
|
R2_demand
|
100
|
0
|
0.513
|
0.142
|
0.085
|
0.535
|
0.744
|
|
|
R2_supply
|
100
|
0
|
0.509
|
0.118
|
0.191
|
0.521
|
0.762
|
|
\(n = 200\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.044
|
0.566
|
8.881
|
10.032
|
11.537
|
|
|
alpha1_hat
|
100
|
0
|
1.174
|
1.117
|
−1.140
|
0.994
|
4.438
|
|
|
alpha2_hat
|
100
|
0
|
0.489
|
0.121
|
0.227
|
0.496
|
0.754
|
|
|
alpha3_hat
|
100
|
0
|
1.002
|
0.118
|
0.800
|
0.995
|
1.399
|
|
|
gamma0_hat
|
100
|
0
|
0.951
|
0.752
|
−1.084
|
0.967
|
2.826
|
|
|
gamma1_hat
|
100
|
0
|
1.059
|
1.226
|
−1.989
|
1.206
|
3.678
|
|
|
gamma2_hat
|
100
|
0
|
1.007
|
0.111
|
0.782
|
1.002
|
1.320
|
|
|
gamma3_hat
|
100
|
0
|
1.009
|
0.113
|
0.724
|
1.006
|
1.378
|
|
|
theta_hat
|
100
|
0
|
0.057
|
0.214
|
−0.394
|
0.017
|
0.707
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.217
|
0.940
|
−2.144
|
0.093
|
2.636
|
|
|
R2_demand
|
100
|
0
|
0.510
|
0.116
|
0.133
|
0.530
|
0.706
|
|
|
R2_supply
|
100
|
0
|
0.519
|
0.085
|
0.281
|
0.531
|
0.691
|
|
\(n = 1000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.016
|
0.175
|
9.584
|
10.020
|
10.482
|
|
|
alpha1_hat
|
100
|
0
|
1.003
|
0.360
|
0.058
|
0.995
|
1.761
|
|
|
alpha2_hat
|
100
|
0
|
0.501
|
0.041
|
0.418
|
0.497
|
0.596
|
|
|
alpha3_hat
|
100
|
0
|
1.004
|
0.044
|
0.928
|
1.001
|
1.117
|
|
|
gamma0_hat
|
100
|
0
|
0.993
|
0.262
|
0.376
|
0.990
|
1.768
|
|
|
gamma1_hat
|
100
|
0
|
1.031
|
0.453
|
0.014
|
1.033
|
2.079
|
|
|
gamma2_hat
|
100
|
0
|
0.999
|
0.041
|
0.880
|
1.001
|
1.117
|
|
|
gamma3_hat
|
100
|
0
|
0.996
|
0.043
|
0.879
|
0.996
|
1.117
|
|
|
theta_hat
|
100
|
0
|
0.046
|
0.085
|
−0.204
|
0.040
|
0.230
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.519
|
0.985
|
−2.292
|
0.472
|
2.589
|
|
|
R2_demand
|
100
|
0
|
0.519
|
0.039
|
0.418
|
0.519
|
0.600
|
|
|
R2_supply
|
100
|
0
|
0.521
|
0.033
|
0.447
|
0.523
|
0.582
|
|
\(n = 2000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.012
|
0.137
|
9.681
|
9.998
|
10.394
|
|
|
alpha1_hat
|
100
|
0
|
0.991
|
0.228
|
0.396
|
1.004
|
1.556
|
|
|
alpha2_hat
|
100
|
0
|
0.503
|
0.027
|
0.432
|
0.503
|
0.568
|
|
|
alpha3_hat
|
100
|
0
|
1.005
|
0.031
|
0.929
|
1.009
|
1.097
|
|
|
gamma0_hat
|
100
|
0
|
1.005
|
0.227
|
0.326
|
0.996
|
1.614
|
|
|
gamma1_hat
|
100
|
0
|
0.981
|
0.357
|
0.213
|
1.023
|
1.822
|
|
|
gamma2_hat
|
100
|
0
|
1.000
|
0.036
|
0.923
|
1.002
|
1.124
|
|
|
gamma3_hat
|
100
|
0
|
0.999
|
0.034
|
0.928
|
0.996
|
1.094
|
|
|
theta_hat
|
100
|
0
|
0.051
|
0.064
|
−0.082
|
0.047
|
0.204
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.854
|
1.063
|
−1.409
|
0.789
|
3.143
|
|
|
R2_demand
|
100
|
0
|
0.520
|
0.031
|
0.432
|
0.520
|
0.580
|
|
|
R2_supply
|
100
|
0
|
0.525
|
0.026
|
0.453
|
0.527
|
0.574
|
|
\(\alpha_2 =
1.0\)
\(n = 50\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.933
|
0.897
|
7.453
|
9.922
|
12.191
|
|
|
alpha1_hat
|
100
|
0
|
0.943
|
3.335
|
−7.741
|
1.125
|
8.999
|
|
|
alpha2_hat
|
100
|
0
|
0.990
|
0.372
|
−0.355
|
0.966
|
1.926
|
|
|
alpha3_hat
|
100
|
0
|
0.992
|
0.218
|
0.563
|
0.996
|
1.477
|
|
|
gamma0_hat
|
100
|
0
|
0.640
|
2.061
|
−14.446
|
1.015
|
4.087
|
|
|
gamma1_hat
|
100
|
0
|
1.554
|
4.534
|
−18.420
|
1.443
|
16.969
|
|
|
gamma2_hat
|
100
|
0
|
1.059
|
0.302
|
0.575
|
1.000
|
3.281
|
|
|
gamma3_hat
|
100
|
0
|
1.069
|
0.261
|
0.610
|
1.043
|
2.256
|
|
|
theta_hat
|
100
|
0
|
0.052
|
0.626
|
−2.284
|
0.004
|
2.942
|
|
|
theta_hat_t_stats
|
100
|
0
|
−0.081
|
1.062
|
−2.654
|
0.020
|
1.924
|
|
|
R2_demand
|
100
|
0
|
0.599
|
0.163
|
−0.154
|
0.641
|
0.834
|
|
|
R2_supply
|
100
|
0
|
0.526
|
0.390
|
−2.942
|
0.590
|
0.827
|
|
\(n = 100\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.938
|
0.640
|
8.767
|
9.912
|
11.649
|
|
|
alpha1_hat
|
100
|
0
|
1.277
|
2.296
|
−3.572
|
1.307
|
9.090
|
|
|
alpha2_hat
|
100
|
0
|
0.957
|
0.243
|
0.171
|
0.962
|
1.500
|
|
|
alpha3_hat
|
100
|
0
|
0.996
|
0.141
|
0.591
|
0.976
|
1.348
|
|
|
gamma0_hat
|
100
|
0
|
0.750
|
1.261
|
−4.133
|
0.881
|
3.111
|
|
|
gamma1_hat
|
100
|
0
|
0.659
|
2.761
|
−10.647
|
0.663
|
7.674
|
|
|
gamma2_hat
|
100
|
0
|
1.029
|
0.177
|
0.625
|
1.014
|
1.746
|
|
|
gamma3_hat
|
100
|
0
|
1.012
|
0.174
|
0.624
|
0.990
|
1.609
|
|
|
theta_hat
|
100
|
0
|
0.116
|
0.303
|
−0.539
|
0.074
|
1.304
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.282
|
0.945
|
−1.705
|
0.294
|
2.841
|
|
|
R2_demand
|
100
|
0
|
0.562
|
0.128
|
0.062
|
0.583
|
0.757
|
|
|
R2_supply
|
100
|
0
|
0.543
|
0.141
|
0.048
|
0.556
|
0.810
|
|
\(n = 200\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.007
|
0.499
|
8.849
|
9.898
|
12.162
|
|
|
alpha1_hat
|
100
|
0
|
1.156
|
1.481
|
−2.597
|
1.140
|
5.041
|
|
|
alpha2_hat
|
100
|
0
|
0.986
|
0.184
|
0.567
|
0.987
|
1.489
|
|
|
alpha3_hat
|
100
|
0
|
0.997
|
0.102
|
0.805
|
0.980
|
1.371
|
|
|
gamma0_hat
|
100
|
0
|
0.951
|
0.702
|
−0.596
|
0.977
|
2.583
|
|
|
gamma1_hat
|
100
|
0
|
1.142
|
1.640
|
−3.068
|
1.222
|
5.098
|
|
|
gamma2_hat
|
100
|
0
|
1.012
|
0.100
|
0.806
|
1.008
|
1.282
|
|
|
gamma3_hat
|
100
|
0
|
1.010
|
0.102
|
0.796
|
1.011
|
1.316
|
|
|
theta_hat
|
100
|
0
|
0.039
|
0.159
|
−0.323
|
0.032
|
0.481
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.207
|
0.903
|
−1.874
|
0.217
|
2.135
|
|
|
R2_demand
|
100
|
0
|
0.570
|
0.128
|
−0.289
|
0.581
|
0.734
|
|
|
R2_supply
|
100
|
0
|
0.575
|
0.078
|
0.370
|
0.579
|
0.739
|
|
\(n = 1000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.006
|
0.190
|
9.664
|
10.007
|
10.476
|
|
|
alpha1_hat
|
100
|
0
|
1.074
|
0.713
|
−0.916
|
1.075
|
3.064
|
|
|
alpha2_hat
|
100
|
0
|
0.994
|
0.084
|
0.760
|
0.989
|
1.234
|
|
|
alpha3_hat
|
100
|
0
|
0.998
|
0.048
|
0.896
|
0.995
|
1.125
|
|
|
gamma0_hat
|
100
|
0
|
1.022
|
0.287
|
0.150
|
1.027
|
1.582
|
|
|
gamma1_hat
|
100
|
0
|
0.969
|
0.670
|
−1.149
|
1.006
|
2.646
|
|
|
gamma2_hat
|
100
|
0
|
0.996
|
0.043
|
0.874
|
0.992
|
1.111
|
|
|
gamma3_hat
|
100
|
0
|
1.009
|
0.040
|
0.916
|
1.009
|
1.120
|
|
|
theta_hat
|
100
|
0
|
0.052
|
0.072
|
−0.154
|
0.052
|
0.304
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.666
|
0.959
|
−2.192
|
0.690
|
3.611
|
|
|
R2_demand
|
100
|
0
|
0.570
|
0.032
|
0.490
|
0.574
|
0.662
|
|
|
R2_supply
|
100
|
0
|
0.578
|
0.036
|
0.493
|
0.578
|
0.655
|
|
\(n = 2000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.010
|
0.126
|
9.731
|
9.995
|
10.335
|
|
|
alpha1_hat
|
100
|
0
|
1.019
|
0.463
|
0.015
|
1.021
|
2.032
|
|
|
alpha2_hat
|
100
|
0
|
1.000
|
0.053
|
0.850
|
1.000
|
1.129
|
|
|
alpha3_hat
|
100
|
0
|
1.003
|
0.031
|
0.938
|
1.005
|
1.062
|
|
|
gamma0_hat
|
100
|
0
|
0.988
|
0.220
|
0.492
|
0.992
|
1.562
|
|
|
gamma1_hat
|
100
|
0
|
0.960
|
0.521
|
−0.133
|
0.954
|
2.213
|
|
|
gamma2_hat
|
100
|
0
|
1.003
|
0.032
|
0.919
|
1.006
|
1.068
|
|
|
gamma3_hat
|
100
|
0
|
0.998
|
0.029
|
0.913
|
0.995
|
1.085
|
|
|
theta_hat
|
100
|
0
|
0.054
|
0.049
|
−0.057
|
0.050
|
0.160
|
|
|
theta_hat_t_stats
|
100
|
0
|
1.018
|
0.926
|
−1.117
|
0.947
|
3.062
|
|
|
R2_demand
|
100
|
0
|
0.571
|
0.024
|
0.493
|
0.572
|
0.614
|
|
|
R2_supply
|
100
|
0
|
0.573
|
0.025
|
0.491
|
0.574
|
0.617
|
|
\(\alpha_2 =
5.0\)
\(n = 50\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.027
|
0.973
|
8.184
|
9.967
|
14.140
|
|
|
alpha1_hat
|
100
|
0
|
2.793
|
15.115
|
−34.879
|
2.222
|
36.412
|
|
|
alpha2_hat
|
100
|
0
|
4.848
|
1.764
|
1.841
|
4.817
|
9.933
|
|
|
alpha3_hat
|
100
|
0
|
1.004
|
0.222
|
0.481
|
0.970
|
1.743
|
|
|
gamma0_hat
|
100
|
0
|
0.904
|
1.700
|
−4.256
|
1.140
|
3.702
|
|
|
gamma1_hat
|
100
|
0
|
3.342
|
16.518
|
−32.573
|
3.749
|
46.579
|
|
|
gamma2_hat
|
100
|
0
|
0.987
|
0.221
|
0.530
|
0.970
|
1.602
|
|
|
gamma3_hat
|
100
|
0
|
1.025
|
0.255
|
0.477
|
1.000
|
2.254
|
|
|
theta_hat
|
100
|
0
|
0.035
|
0.415
|
−0.927
|
−0.009
|
1.357
|
|
|
theta_hat_t_stats
|
100
|
0
|
−0.062
|
0.940
|
−1.957
|
−0.037
|
1.841
|
|
|
R2_demand
|
100
|
0
|
0.591
|
0.189
|
−0.415
|
0.620
|
0.827
|
|
|
R2_supply
|
100
|
0
|
0.579
|
0.232
|
−0.457
|
0.651
|
0.843
|
|
\(n = 100\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.961
|
0.545
|
8.679
|
9.945
|
11.240
|
|
|
alpha1_hat
|
100
|
0
|
1.358
|
8.303
|
−18.125
|
1.695
|
18.536
|
|
|
alpha2_hat
|
100
|
0
|
4.939
|
0.965
|
2.676
|
4.963
|
7.482
|
|
|
alpha3_hat
|
100
|
0
|
0.994
|
0.134
|
0.628
|
0.996
|
1.392
|
|
|
gamma0_hat
|
100
|
0
|
0.870
|
0.891
|
−2.312
|
0.924
|
2.966
|
|
|
gamma1_hat
|
100
|
0
|
−1.595
|
10.364
|
−32.843
|
−1.492
|
21.853
|
|
|
gamma2_hat
|
100
|
0
|
1.018
|
0.133
|
0.716
|
1.011
|
1.456
|
|
|
gamma3_hat
|
100
|
0
|
1.023
|
0.151
|
0.691
|
1.036
|
1.395
|
|
|
theta_hat
|
100
|
0
|
0.121
|
0.227
|
−0.359
|
0.120
|
0.947
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.443
|
0.912
|
−2.061
|
0.546
|
2.856
|
|
|
R2_demand
|
100
|
0
|
0.622
|
0.105
|
0.291
|
0.640
|
0.816
|
|
|
R2_supply
|
100
|
0
|
0.611
|
0.108
|
0.320
|
0.618
|
0.804
|
|
\(n = 200\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.967
|
0.396
|
9.046
|
9.941
|
10.802
|
|
|
alpha1_hat
|
100
|
0
|
0.952
|
7.211
|
−15.549
|
1.057
|
18.070
|
|
|
alpha2_hat
|
100
|
0
|
4.972
|
0.807
|
3.013
|
4.915
|
6.846
|
|
|
alpha3_hat
|
100
|
0
|
1.001
|
0.099
|
0.769
|
0.993
|
1.269
|
|
|
gamma0_hat
|
100
|
0
|
1.000
|
0.728
|
−0.759
|
1.040
|
2.401
|
|
|
gamma1_hat
|
100
|
0
|
1.201
|
7.393
|
−16.017
|
0.730
|
22.576
|
|
|
gamma2_hat
|
100
|
0
|
0.997
|
0.105
|
0.778
|
0.991
|
1.339
|
|
|
gamma3_hat
|
100
|
0
|
1.008
|
0.109
|
0.781
|
0.998
|
1.265
|
|
|
theta_hat
|
100
|
0
|
0.052
|
0.179
|
−0.443
|
0.026
|
0.470
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.214
|
1.078
|
−2.563
|
0.218
|
2.362
|
|
|
R2_demand
|
100
|
0
|
0.620
|
0.068
|
0.439
|
0.633
|
0.746
|
|
|
R2_supply
|
100
|
0
|
0.614
|
0.077
|
0.318
|
0.629
|
0.733
|
|
\(n = 1000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.021
|
0.196
|
9.574
|
9.984
|
10.626
|
|
|
alpha1_hat
|
100
|
0
|
1.292
|
2.799
|
−5.567
|
0.953
|
9.036
|
|
|
alpha2_hat
|
100
|
0
|
4.988
|
0.341
|
4.140
|
4.967
|
5.810
|
|
|
alpha3_hat
|
100
|
0
|
1.001
|
0.047
|
0.903
|
1.002
|
1.120
|
|
|
gamma0_hat
|
100
|
0
|
1.023
|
0.296
|
0.171
|
1.025
|
1.626
|
|
|
gamma1_hat
|
100
|
0
|
0.913
|
3.009
|
−5.073
|
1.151
|
8.242
|
|
|
gamma2_hat
|
100
|
0
|
0.996
|
0.043
|
0.900
|
0.994
|
1.111
|
|
|
gamma3_hat
|
100
|
0
|
1.002
|
0.046
|
0.881
|
0.998
|
1.107
|
|
|
theta_hat
|
100
|
0
|
0.049
|
0.069
|
−0.114
|
0.044
|
0.193
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.717
|
1.039
|
−1.909
|
0.685
|
2.878
|
|
|
R2_demand
|
100
|
0
|
0.617
|
0.036
|
0.502
|
0.619
|
0.691
|
|
|
R2_supply
|
100
|
0
|
0.626
|
0.030
|
0.552
|
0.627
|
0.698
|
|
\(n = 2000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.003
|
0.139
|
9.664
|
9.999
|
10.391
|
|
|
alpha1_hat
|
100
|
0
|
0.892
|
1.788
|
−4.114
|
0.834
|
4.986
|
|
|
alpha2_hat
|
100
|
0
|
5.011
|
0.207
|
4.459
|
5.035
|
5.508
|
|
|
alpha3_hat
|
100
|
0
|
0.999
|
0.029
|
0.933
|
0.997
|
1.060
|
|
|
gamma0_hat
|
100
|
0
|
1.027
|
0.191
|
0.554
|
1.038
|
1.529
|
|
|
gamma1_hat
|
100
|
0
|
0.824
|
2.086
|
−5.515
|
0.945
|
6.108
|
|
|
gamma2_hat
|
100
|
0
|
0.998
|
0.028
|
0.927
|
0.999
|
1.073
|
|
|
gamma3_hat
|
100
|
0
|
0.997
|
0.032
|
0.924
|
0.995
|
1.068
|
|
|
theta_hat
|
100
|
0
|
0.050
|
0.046
|
−0.063
|
0.052
|
0.192
|
|
|
theta_hat_t_stats
|
100
|
0
|
1.057
|
0.982
|
−1.450
|
1.124
|
3.838
|
|
|
R2_demand
|
100
|
0
|
0.619
|
0.023
|
0.550
|
0.624
|
0.662
|
|
|
R2_supply
|
100
|
0
|
0.623
|
0.020
|
0.575
|
0.623
|
0.669
|
|
\(\alpha_2 =
20.0\)
\(n = 50\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.078
|
1.156
|
7.657
|
10.040
|
17.632
|
|
|
alpha1_hat
|
100
|
0
|
2.394
|
47.415
|
−116.140
|
1.858
|
116.686
|
|
|
alpha2_hat
|
100
|
0
|
20.067
|
5.963
|
8.920
|
19.537
|
49.105
|
|
|
alpha3_hat
|
100
|
0
|
1.028
|
0.243
|
0.532
|
0.999
|
2.502
|
|
|
gamma0_hat
|
100
|
0
|
1.099
|
1.335
|
−5.080
|
1.365
|
3.467
|
|
|
gamma1_hat
|
100
|
0
|
11.897
|
57.608
|
−94.735
|
18.775
|
208.804
|
|
|
gamma2_hat
|
100
|
0
|
0.987
|
0.216
|
0.494
|
0.972
|
1.955
|
|
|
gamma3_hat
|
100
|
0
|
0.983
|
0.224
|
0.552
|
0.945
|
1.687
|
|
|
theta_hat
|
100
|
0
|
−0.012
|
0.361
|
−1.222
|
−0.025
|
1.432
|
|
|
theta_hat_t_stats
|
100
|
0
|
−0.133
|
0.987
|
−2.743
|
−0.090
|
1.916
|
|
|
R2_demand
|
100
|
0
|
0.564
|
0.537
|
−4.527
|
0.655
|
0.827
|
|
|
R2_supply
|
100
|
0
|
0.630
|
0.146
|
0.159
|
0.652
|
0.837
|
|
\(n = 100\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.000
|
0.682
|
8.803
|
9.929
|
12.743
|
|
|
alpha1_hat
|
100
|
0
|
2.544
|
33.319
|
−74.863
|
0.205
|
79.604
|
|
|
alpha2_hat
|
100
|
0
|
19.850
|
3.830
|
11.814
|
20.057
|
30.398
|
|
|
alpha3_hat
|
100
|
0
|
0.992
|
0.157
|
0.692
|
0.984
|
1.611
|
|
|
gamma0_hat
|
100
|
0
|
0.911
|
0.894
|
−1.489
|
0.976
|
2.832
|
|
|
gamma1_hat
|
100
|
0
|
−0.519
|
40.158
|
−115.921
|
−0.394
|
114.922
|
|
|
gamma2_hat
|
100
|
0
|
1.021
|
0.138
|
0.680
|
1.028
|
1.385
|
|
|
gamma3_hat
|
100
|
0
|
1.006
|
0.140
|
0.695
|
0.998
|
1.461
|
|
|
theta_hat
|
100
|
0
|
0.067
|
0.216
|
−0.399
|
0.048
|
0.700
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.207
|
0.973
|
−2.418
|
0.258
|
2.427
|
|
|
R2_demand
|
100
|
0
|
0.618
|
0.129
|
−0.022
|
0.636
|
0.788
|
|
|
R2_supply
|
100
|
0
|
0.630
|
0.104
|
0.224
|
0.646
|
0.817
|
|
\(n = 200\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.994
|
0.371
|
9.163
|
10.035
|
11.065
|
|
|
alpha1_hat
|
100
|
0
|
0.532
|
21.853
|
−67.392
|
−0.577
|
48.025
|
|
|
alpha2_hat
|
100
|
0
|
20.039
|
2.642
|
13.664
|
20.145
|
27.673
|
|
|
alpha3_hat
|
100
|
0
|
0.991
|
0.103
|
0.703
|
1.002
|
1.231
|
|
|
gamma0_hat
|
100
|
0
|
0.994
|
0.802
|
−1.146
|
1.086
|
2.491
|
|
|
gamma1_hat
|
100
|
0
|
3.179
|
21.209
|
−59.636
|
3.509
|
66.693
|
|
|
gamma2_hat
|
100
|
0
|
1.008
|
0.110
|
0.778
|
0.990
|
1.279
|
|
|
gamma3_hat
|
100
|
0
|
1.004
|
0.107
|
0.793
|
0.991
|
1.428
|
|
|
theta_hat
|
100
|
0
|
0.037
|
0.144
|
−0.300
|
0.038
|
0.415
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.170
|
0.935
|
−2.326
|
0.258
|
2.641
|
|
|
R2_demand
|
100
|
0
|
0.633
|
0.073
|
0.391
|
0.644
|
0.773
|
|
|
R2_supply
|
100
|
0
|
0.632
|
0.073
|
0.423
|
0.641
|
0.767
|
|
\(n = 1000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.019
|
0.174
|
9.616
|
10.026
|
10.367
|
|
|
alpha1_hat
|
100
|
0
|
−0.831
|
10.322
|
−28.642
|
−1.953
|
26.857
|
|
|
alpha2_hat
|
100
|
0
|
20.251
|
1.177
|
16.694
|
20.211
|
23.084
|
|
|
alpha3_hat
|
100
|
0
|
1.006
|
0.041
|
0.912
|
1.012
|
1.103
|
|
|
gamma0_hat
|
100
|
0
|
0.964
|
0.300
|
0.199
|
0.960
|
1.919
|
|
|
gamma1_hat
|
100
|
0
|
−1.540
|
10.888
|
−31.544
|
−2.235
|
25.781
|
|
|
gamma2_hat
|
100
|
0
|
1.008
|
0.043
|
0.883
|
1.004
|
1.144
|
|
|
gamma3_hat
|
100
|
0
|
1.001
|
0.045
|
0.859
|
1.001
|
1.124
|
|
|
theta_hat
|
100
|
0
|
0.065
|
0.064
|
−0.073
|
0.064
|
0.204
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.983
|
0.966
|
−1.289
|
0.993
|
3.082
|
|
|
R2_demand
|
100
|
0
|
0.634
|
0.028
|
0.545
|
0.635
|
0.696
|
|
|
R2_supply
|
100
|
0
|
0.631
|
0.031
|
0.539
|
0.633
|
0.692
|
|
\(n = 2000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.999
|
0.137
|
9.610
|
10.001
|
10.327
|
|
|
alpha1_hat
|
100
|
0
|
1.356
|
8.204
|
−15.540
|
0.259
|
21.595
|
|
|
alpha2_hat
|
100
|
0
|
19.974
|
0.969
|
18.050
|
19.986
|
22.431
|
|
|
alpha3_hat
|
100
|
0
|
1.004
|
0.032
|
0.889
|
1.004
|
1.073
|
|
|
gamma0_hat
|
100
|
0
|
1.013
|
0.197
|
0.398
|
1.013
|
1.388
|
|
|
gamma1_hat
|
100
|
0
|
1.539
|
7.142
|
−15.781
|
1.533
|
22.144
|
|
|
gamma2_hat
|
100
|
0
|
1.000
|
0.031
|
0.932
|
0.999
|
1.092
|
|
|
gamma3_hat
|
100
|
0
|
0.997
|
0.033
|
0.912
|
0.993
|
1.077
|
|
|
theta_hat
|
100
|
0
|
0.045
|
0.041
|
−0.050
|
0.047
|
0.141
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.983
|
0.887
|
−1.082
|
1.037
|
3.040
|
|
|
R2_demand
|
100
|
0
|
0.630
|
0.022
|
0.580
|
0.629
|
0.688
|
|
|
R2_supply
|
100
|
0
|
0.632
|
0.021
|
0.576
|
0.634
|
0.673
|
|
\(\theta =
0.1\)
\(\alpha_2 =
0.1\)
\(n = 50\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.922
|
1.004
|
7.786
|
9.863
|
14.467
|
|
|
alpha1_hat
|
100
|
0
|
0.980
|
0.866
|
−0.802
|
0.867
|
3.118
|
|
|
alpha2_hat
|
100
|
0
|
0.097
|
0.084
|
−0.101
|
0.096
|
0.362
|
|
|
alpha3_hat
|
100
|
0
|
0.993
|
0.247
|
0.475
|
0.952
|
2.143
|
|
|
gamma0_hat
|
100
|
0
|
0.696
|
1.897
|
−6.221
|
1.122
|
4.230
|
|
|
gamma1_hat
|
100
|
0
|
0.268
|
6.858
|
−39.767
|
0.995
|
20.044
|
|
|
gamma2_hat
|
100
|
0
|
1.029
|
0.259
|
0.404
|
0.976
|
1.805
|
|
|
gamma3_hat
|
100
|
0
|
1.045
|
0.267
|
0.450
|
1.008
|
1.922
|
|
|
theta_hat
|
100
|
0
|
0.585
|
3.766
|
−8.145
|
0.146
|
22.392
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.144
|
1.034
|
−2.194
|
0.184
|
3.212
|
|
|
R2_demand
|
100
|
0
|
0.313
|
0.320
|
−1.342
|
0.399
|
0.705
|
|
|
R2_supply
|
100
|
0
|
0.256
|
0.428
|
−2.808
|
0.364
|
0.755
|
|
\(n = 100\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.982
|
0.793
|
8.536
|
9.913
|
14.488
|
|
|
alpha1_hat
|
100
|
0
|
0.983
|
0.706
|
−0.476
|
0.892
|
4.420
|
|
|
alpha2_hat
|
100
|
0
|
0.101
|
0.061
|
−0.055
|
0.101
|
0.364
|
|
|
alpha3_hat
|
100
|
0
|
0.998
|
0.183
|
0.695
|
0.974
|
2.060
|
|
|
gamma0_hat
|
100
|
0
|
0.951
|
0.981
|
−3.125
|
0.974
|
3.052
|
|
|
gamma1_hat
|
100
|
0
|
1.664
|
7.218
|
−18.935
|
1.102
|
56.585
|
|
|
gamma2_hat
|
100
|
0
|
1.005
|
0.144
|
0.694
|
1.005
|
1.527
|
|
|
gamma3_hat
|
100
|
0
|
1.008
|
0.161
|
0.585
|
0.980
|
1.368
|
|
|
theta_hat
|
100
|
0
|
0.002
|
2.669
|
−15.902
|
0.117
|
11.026
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.215
|
1.044
|
−2.261
|
0.120
|
2.577
|
|
|
R2_demand
|
100
|
0
|
0.279
|
0.311
|
−2.128
|
0.345
|
0.582
|
|
|
R2_supply
|
100
|
0
|
0.293
|
0.171
|
−0.510
|
0.311
|
0.622
|
|
\(n = 200\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.017
|
0.514
|
8.751
|
9.988
|
11.461
|
|
|
alpha1_hat
|
100
|
0
|
1.064
|
0.383
|
0.235
|
1.066
|
1.977
|
|
|
alpha2_hat
|
100
|
0
|
0.094
|
0.040
|
0.005
|
0.091
|
0.220
|
|
|
alpha3_hat
|
100
|
0
|
1.007
|
0.101
|
0.823
|
0.997
|
1.310
|
|
|
gamma0_hat
|
100
|
0
|
0.861
|
0.777
|
−1.152
|
0.850
|
2.406
|
|
|
gamma1_hat
|
100
|
0
|
0.916
|
1.588
|
−10.603
|
1.041
|
5.889
|
|
|
gamma2_hat
|
100
|
0
|
1.013
|
0.111
|
0.809
|
1.003
|
1.346
|
|
|
gamma3_hat
|
100
|
0
|
1.023
|
0.114
|
0.790
|
1.024
|
1.432
|
|
|
theta_hat
|
100
|
0
|
0.160
|
0.803
|
−2.355
|
0.113
|
5.796
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.265
|
1.075
|
−2.432
|
0.237
|
3.224
|
|
|
R2_demand
|
100
|
0
|
0.310
|
0.134
|
−0.144
|
0.327
|
0.574
|
|
|
R2_supply
|
100
|
0
|
0.296
|
0.146
|
−0.257
|
0.321
|
0.568
|
|
\(n = 1000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.008
|
0.185
|
9.641
|
10.009
|
10.470
|
|
|
alpha1_hat
|
100
|
0
|
0.987
|
0.168
|
0.606
|
0.985
|
1.521
|
|
|
alpha2_hat
|
100
|
0
|
0.102
|
0.016
|
0.055
|
0.102
|
0.131
|
|
|
alpha3_hat
|
100
|
0
|
0.998
|
0.046
|
0.873
|
0.998
|
1.120
|
|
|
gamma0_hat
|
100
|
0
|
0.991
|
0.326
|
0.062
|
1.004
|
1.792
|
|
|
gamma1_hat
|
100
|
0
|
1.052
|
0.348
|
0.132
|
1.088
|
1.913
|
|
|
gamma2_hat
|
100
|
0
|
0.999
|
0.044
|
0.899
|
0.999
|
1.099
|
|
|
gamma3_hat
|
100
|
0
|
1.002
|
0.051
|
0.881
|
1.003
|
1.119
|
|
|
theta_hat
|
100
|
0
|
0.076
|
0.187
|
−0.354
|
0.068
|
0.628
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.412
|
1.084
|
−2.290
|
0.453
|
3.714
|
|
|
R2_demand
|
100
|
0
|
0.313
|
0.051
|
0.186
|
0.323
|
0.403
|
|
|
R2_supply
|
100
|
0
|
0.313
|
0.058
|
0.146
|
0.313
|
0.448
|
|
\(n = 2000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.998
|
0.150
|
9.650
|
10.002
|
10.424
|
|
|
alpha1_hat
|
100
|
0
|
0.987
|
0.123
|
0.569
|
0.993
|
1.312
|
|
|
alpha2_hat
|
100
|
0
|
0.101
|
0.012
|
0.072
|
0.101
|
0.125
|
|
|
alpha3_hat
|
100
|
0
|
1.001
|
0.036
|
0.910
|
1.001
|
1.110
|
|
|
gamma0_hat
|
100
|
0
|
0.970
|
0.226
|
0.345
|
0.960
|
1.502
|
|
|
gamma1_hat
|
100
|
0
|
0.992
|
0.252
|
0.176
|
1.006
|
1.554
|
|
|
gamma2_hat
|
100
|
0
|
1.004
|
0.034
|
0.920
|
1.001
|
1.104
|
|
|
gamma3_hat
|
100
|
0
|
1.004
|
0.032
|
0.922
|
1.008
|
1.082
|
|
|
theta_hat
|
100
|
0
|
0.110
|
0.131
|
−0.196
|
0.093
|
0.498
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.872
|
1.015
|
−1.513
|
0.796
|
3.817
|
|
|
R2_demand
|
100
|
0
|
0.312
|
0.040
|
0.198
|
0.314
|
0.415
|
|
|
R2_supply
|
100
|
0
|
0.311
|
0.037
|
0.234
|
0.316
|
0.405
|
|
\(\alpha_2 =
0.5\)
\(n = 50\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.978
|
1.100
|
7.673
|
9.744
|
14.551
|
|
|
alpha1_hat
|
100
|
0
|
1.068
|
2.043
|
−3.604
|
1.104
|
9.409
|
|
|
alpha2_hat
|
100
|
0
|
0.491
|
0.222
|
−0.065
|
0.470
|
1.043
|
|
|
alpha3_hat
|
100
|
0
|
0.979
|
0.220
|
0.433
|
0.949
|
1.703
|
|
|
gamma0_hat
|
100
|
0
|
0.801
|
1.611
|
−3.806
|
1.089
|
4.233
|
|
|
gamma1_hat
|
100
|
0
|
38.189
|
374.984
|
−31.951
|
1.125
|
3750.284
|
|
|
gamma2_hat
|
100
|
0
|
1.021
|
0.222
|
0.652
|
0.990
|
1.638
|
|
|
gamma3_hat
|
100
|
0
|
1.023
|
0.223
|
0.481
|
0.998
|
1.602
|
|
|
theta_hat
|
100
|
0
|
−8.140
|
83.354
|
−833.306
|
0.038
|
6.903
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.146
|
0.938
|
−2.223
|
0.108
|
2.629
|
|
|
R2_demand
|
100
|
0
|
0.441
|
0.308
|
−1.486
|
0.501
|
0.798
|
|
|
R2_supply
|
100
|
0
|
0.464
|
0.212
|
−0.390
|
0.518
|
0.820
|
|
\(n = 100\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.938
|
0.726
|
8.691
|
9.844
|
12.232
|
|
|
alpha1_hat
|
100
|
0
|
1.088
|
1.283
|
−2.326
|
1.066
|
5.789
|
|
|
alpha2_hat
|
100
|
0
|
0.484
|
0.140
|
0.028
|
0.491
|
0.981
|
|
|
alpha3_hat
|
100
|
0
|
0.991
|
0.157
|
0.605
|
0.962
|
1.598
|
|
|
gamma0_hat
|
100
|
0
|
1.110
|
0.972
|
−1.632
|
1.195
|
3.511
|
|
|
gamma1_hat
|
100
|
0
|
0.516
|
4.430
|
−39.831
|
0.874
|
7.488
|
|
|
gamma2_hat
|
100
|
0
|
0.976
|
0.154
|
0.636
|
0.955
|
1.475
|
|
|
gamma3_hat
|
100
|
0
|
0.980
|
0.146
|
0.613
|
0.971
|
1.341
|
|
|
theta_hat
|
100
|
0
|
0.191
|
0.917
|
−0.942
|
0.095
|
8.588
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.275
|
1.017
|
−2.654
|
0.406
|
3.067
|
|
|
R2_demand
|
100
|
0
|
0.469
|
0.192
|
−0.342
|
0.511
|
0.774
|
|
|
R2_supply
|
100
|
0
|
0.495
|
0.114
|
0.205
|
0.512
|
0.705
|
|
\(n = 200\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.041
|
0.475
|
9.076
|
10.000
|
11.728
|
|
|
alpha1_hat
|
100
|
0
|
1.054
|
1.037
|
−1.468
|
0.926
|
3.057
|
|
|
alpha2_hat
|
100
|
0
|
0.500
|
0.112
|
0.204
|
0.497
|
0.780
|
|
|
alpha3_hat
|
100
|
0
|
1.010
|
0.110
|
0.765
|
1.016
|
1.246
|
|
|
gamma0_hat
|
100
|
0
|
0.874
|
0.770
|
−1.888
|
0.993
|
2.677
|
|
|
gamma1_hat
|
100
|
0
|
1.112
|
1.128
|
−1.090
|
1.063
|
4.240
|
|
|
gamma2_hat
|
100
|
0
|
1.019
|
0.116
|
0.767
|
1.014
|
1.350
|
|
|
gamma3_hat
|
100
|
0
|
0.993
|
0.102
|
0.770
|
0.980
|
1.389
|
|
|
theta_hat
|
100
|
0
|
0.094
|
0.214
|
−0.393
|
0.088
|
0.615
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.403
|
1.029
|
−2.875
|
0.385
|
2.805
|
|
|
R2_demand
|
100
|
0
|
0.477
|
0.126
|
−0.315
|
0.500
|
0.643
|
|
|
R2_supply
|
100
|
0
|
0.479
|
0.112
|
0.073
|
0.481
|
0.687
|
|
\(n = 1000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.042
|
0.185
|
9.652
|
10.034
|
10.520
|
|
|
alpha1_hat
|
100
|
0
|
0.969
|
0.399
|
−0.250
|
0.997
|
2.022
|
|
|
alpha2_hat
|
100
|
0
|
0.509
|
0.044
|
0.410
|
0.505
|
0.621
|
|
|
alpha3_hat
|
100
|
0
|
1.014
|
0.047
|
0.912
|
1.011
|
1.141
|
|
|
gamma0_hat
|
100
|
0
|
1.023
|
0.258
|
0.411
|
1.023
|
1.605
|
|
|
gamma1_hat
|
100
|
0
|
0.937
|
0.426
|
−0.057
|
0.947
|
1.992
|
|
|
gamma2_hat
|
100
|
0
|
0.996
|
0.041
|
0.920
|
0.992
|
1.102
|
|
|
gamma3_hat
|
100
|
0
|
1.002
|
0.040
|
0.920
|
1.002
|
1.118
|
|
|
theta_hat
|
100
|
0
|
0.108
|
0.074
|
−0.061
|
0.110
|
0.270
|
|
|
theta_hat_t_stats
|
100
|
0
|
1.252
|
0.847
|
−0.708
|
1.309
|
3.174
|
|
|
R2_demand
|
100
|
0
|
0.480
|
0.045
|
0.378
|
0.482
|
0.572
|
|
|
R2_supply
|
100
|
0
|
0.498
|
0.031
|
0.420
|
0.495
|
0.555
|
|
\(n = 2000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.972
|
0.131
|
9.681
|
9.966
|
10.273
|
|
|
alpha1_hat
|
100
|
0
|
0.966
|
0.276
|
−0.048
|
0.946
|
1.588
|
|
|
alpha2_hat
|
100
|
0
|
0.500
|
0.029
|
0.443
|
0.499
|
0.601
|
|
|
alpha3_hat
|
100
|
0
|
0.997
|
0.031
|
0.923
|
0.993
|
1.096
|
|
|
gamma0_hat
|
100
|
0
|
1.012
|
0.207
|
0.396
|
1.033
|
1.514
|
|
|
gamma1_hat
|
100
|
0
|
0.965
|
0.351
|
0.208
|
0.947
|
1.764
|
|
|
gamma2_hat
|
100
|
0
|
0.999
|
0.028
|
0.933
|
0.997
|
1.081
|
|
|
gamma3_hat
|
100
|
0
|
1.000
|
0.030
|
0.938
|
0.997
|
1.084
|
|
|
theta_hat
|
100
|
0
|
0.105
|
0.062
|
−0.028
|
0.097
|
0.262
|
|
|
theta_hat_t_stats
|
100
|
0
|
1.705
|
0.994
|
−0.422
|
1.604
|
3.981
|
|
|
R2_demand
|
100
|
0
|
0.494
|
0.031
|
0.424
|
0.492
|
0.594
|
|
|
R2_supply
|
100
|
0
|
0.493
|
0.029
|
0.408
|
0.495
|
0.571
|
|
\(\alpha_2 =
1.0\)
\(n = 50\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.038
|
0.939
|
8.563
|
9.859
|
13.464
|
|
|
alpha1_hat
|
100
|
0
|
1.139
|
3.316
|
−7.905
|
0.999
|
9.244
|
|
|
alpha2_hat
|
100
|
0
|
0.998
|
0.364
|
0.259
|
0.969
|
1.958
|
|
|
alpha3_hat
|
100
|
0
|
1.000
|
0.203
|
0.591
|
0.988
|
1.603
|
|
|
gamma0_hat
|
100
|
0
|
0.376
|
2.091
|
−14.550
|
0.795
|
3.760
|
|
|
gamma1_hat
|
100
|
0
|
1.860
|
5.439
|
−14.769
|
2.191
|
24.736
|
|
|
gamma2_hat
|
100
|
0
|
1.071
|
0.292
|
0.610
|
1.017
|
2.916
|
|
|
gamma3_hat
|
100
|
0
|
1.070
|
0.310
|
0.377
|
1.040
|
3.055
|
|
|
theta_hat
|
100
|
0
|
0.137
|
0.584
|
−1.691
|
0.056
|
2.587
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.085
|
0.963
|
−3.160
|
0.183
|
2.192
|
|
|
R2_demand
|
100
|
0
|
0.501
|
0.210
|
−0.175
|
0.550
|
0.766
|
|
|
R2_supply
|
100
|
0
|
0.444
|
0.464
|
−3.432
|
0.529
|
0.766
|
|
\(n = 100\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.998
|
0.699
|
8.589
|
10.008
|
12.681
|
|
|
alpha1_hat
|
100
|
0
|
0.966
|
2.437
|
−7.025
|
0.897
|
6.588
|
|
|
alpha2_hat
|
100
|
0
|
1.004
|
0.283
|
0.358
|
1.009
|
1.796
|
|
|
alpha3_hat
|
100
|
0
|
0.992
|
0.162
|
0.666
|
0.982
|
1.479
|
|
|
gamma0_hat
|
100
|
0
|
0.748
|
0.990
|
−1.939
|
0.766
|
3.205
|
|
|
gamma1_hat
|
100
|
0
|
0.915
|
3.725
|
−13.519
|
1.156
|
11.311
|
|
|
gamma2_hat
|
100
|
0
|
1.033
|
0.153
|
0.603
|
1.022
|
1.462
|
|
|
gamma3_hat
|
100
|
0
|
1.025
|
0.130
|
0.778
|
1.029
|
1.371
|
|
|
theta_hat
|
100
|
0
|
0.145
|
0.384
|
−0.731
|
0.104
|
1.793
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.380
|
1.064
|
−2.135
|
0.468
|
2.402
|
|
|
R2_demand
|
100
|
0
|
0.535
|
0.142
|
0.009
|
0.559
|
0.772
|
|
|
R2_supply
|
100
|
0
|
0.520
|
0.122
|
0.117
|
0.537
|
0.764
|
|
\(n = 200\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.052
|
0.470
|
9.294
|
9.975
|
11.816
|
|
|
alpha1_hat
|
100
|
0
|
0.985
|
1.597
|
−3.600
|
1.158
|
5.063
|
|
|
alpha2_hat
|
100
|
0
|
1.013
|
0.187
|
0.547
|
0.993
|
1.675
|
|
|
alpha3_hat
|
100
|
0
|
1.009
|
0.109
|
0.786
|
1.004
|
1.354
|
|
|
gamma0_hat
|
100
|
0
|
0.961
|
0.587
|
−1.124
|
0.952
|
2.288
|
|
|
gamma1_hat
|
100
|
0
|
0.993
|
1.830
|
−3.805
|
0.966
|
5.987
|
|
|
gamma2_hat
|
100
|
0
|
1.006
|
0.091
|
0.814
|
0.997
|
1.297
|
|
|
gamma3_hat
|
100
|
0
|
1.002
|
0.093
|
0.788
|
1.008
|
1.356
|
|
|
theta_hat
|
100
|
0
|
0.102
|
0.176
|
−0.346
|
0.109
|
0.671
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.548
|
0.931
|
−1.758
|
0.557
|
2.690
|
|
|
R2_demand
|
100
|
0
|
0.529
|
0.112
|
−0.065
|
0.552
|
0.714
|
|
|
R2_supply
|
100
|
0
|
0.530
|
0.090
|
0.140
|
0.546
|
0.671
|
|
\(n = 1000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.016
|
0.198
|
9.512
|
9.995
|
10.631
|
|
|
alpha1_hat
|
100
|
0
|
1.035
|
0.685
|
−1.053
|
1.009
|
3.025
|
|
|
alpha2_hat
|
100
|
0
|
0.999
|
0.082
|
0.797
|
1.003
|
1.248
|
|
|
alpha3_hat
|
100
|
0
|
0.997
|
0.049
|
0.896
|
0.992
|
1.156
|
|
|
gamma0_hat
|
100
|
0
|
0.962
|
0.344
|
0.164
|
0.957
|
1.892
|
|
|
gamma1_hat
|
100
|
0
|
1.096
|
0.806
|
−0.830
|
1.103
|
2.837
|
|
|
gamma2_hat
|
100
|
0
|
1.004
|
0.050
|
0.886
|
1.007
|
1.116
|
|
|
gamma3_hat
|
100
|
0
|
0.997
|
0.048
|
0.864
|
0.997
|
1.141
|
|
|
theta_hat
|
100
|
0
|
0.097
|
0.084
|
−0.096
|
0.100
|
0.272
|
|
|
theta_hat_t_stats
|
100
|
0
|
1.216
|
1.050
|
−1.298
|
1.289
|
3.237
|
|
|
R2_demand
|
100
|
0
|
0.529
|
0.041
|
0.420
|
0.531
|
0.624
|
|
|
R2_supply
|
100
|
0
|
0.528
|
0.037
|
0.463
|
0.526
|
0.634
|
|
\(n = 2000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.994
|
0.127
|
9.689
|
9.981
|
10.334
|
|
|
alpha1_hat
|
100
|
0
|
1.076
|
0.462
|
0.143
|
1.053
|
2.293
|
|
|
alpha2_hat
|
100
|
0
|
0.991
|
0.046
|
0.883
|
0.987
|
1.095
|
|
|
alpha3_hat
|
100
|
0
|
1.002
|
0.031
|
0.902
|
1.001
|
1.075
|
|
|
gamma0_hat
|
100
|
0
|
1.013
|
0.208
|
0.495
|
1.007
|
1.482
|
|
|
gamma1_hat
|
100
|
0
|
0.957
|
0.511
|
−0.863
|
0.995
|
2.257
|
|
|
gamma2_hat
|
100
|
0
|
1.000
|
0.029
|
0.922
|
1.001
|
1.081
|
|
|
gamma3_hat
|
100
|
0
|
0.996
|
0.033
|
0.923
|
0.996
|
1.069
|
|
|
theta_hat
|
100
|
0
|
0.101
|
0.052
|
−0.046
|
0.094
|
0.284
|
|
|
theta_hat_t_stats
|
100
|
0
|
1.840
|
0.920
|
−0.871
|
1.732
|
4.718
|
|
|
R2_demand
|
100
|
0
|
0.540
|
0.023
|
0.480
|
0.543
|
0.612
|
|
|
R2_supply
|
100
|
0
|
0.539
|
0.026
|
0.469
|
0.538
|
0.600
|
|
\(\alpha_2 =
5.0\)
\(n = 50\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.972
|
0.721
|
8.034
|
9.826
|
12.227
|
|
|
alpha1_hat
|
100
|
0
|
0.732
|
12.626
|
−30.189
|
1.279
|
31.383
|
|
|
alpha2_hat
|
100
|
0
|
5.012
|
1.345
|
2.416
|
4.866
|
8.509
|
|
|
alpha3_hat
|
100
|
0
|
1.007
|
0.213
|
0.575
|
0.995
|
1.646
|
|
|
gamma0_hat
|
100
|
0
|
0.651
|
2.007
|
−7.080
|
1.176
|
3.719
|
|
|
gamma1_hat
|
100
|
0
|
0.163
|
15.866
|
−44.945
|
0.729
|
35.737
|
|
|
gamma2_hat
|
100
|
0
|
1.039
|
0.290
|
0.616
|
0.990
|
2.241
|
|
|
gamma3_hat
|
100
|
0
|
1.038
|
0.251
|
0.606
|
1.001
|
1.983
|
|
|
theta_hat
|
100
|
0
|
0.150
|
0.404
|
−0.480
|
0.078
|
1.966
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.231
|
0.916
|
−1.868
|
0.318
|
1.936
|
|
|
R2_demand
|
100
|
0
|
0.563
|
0.203
|
−0.275
|
0.602
|
0.819
|
|
|
R2_supply
|
100
|
0
|
0.558
|
0.249
|
−0.887
|
0.633
|
0.817
|
|
\(n = 100\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.938
|
0.567
|
8.736
|
9.990
|
11.303
|
|
|
alpha1_hat
|
100
|
0
|
1.609
|
10.753
|
−29.624
|
1.950
|
38.203
|
|
|
alpha2_hat
|
100
|
0
|
4.877
|
1.207
|
1.285
|
4.847
|
9.029
|
|
|
alpha3_hat
|
100
|
0
|
1.003
|
0.133
|
0.770
|
0.995
|
1.363
|
|
|
gamma0_hat
|
100
|
0
|
0.889
|
0.935
|
−2.240
|
0.995
|
3.073
|
|
|
gamma1_hat
|
100
|
0
|
−0.993
|
11.173
|
−57.032
|
−0.681
|
25.385
|
|
|
gamma2_hat
|
100
|
0
|
1.017
|
0.137
|
0.690
|
0.991
|
1.433
|
|
|
gamma3_hat
|
100
|
0
|
1.031
|
0.155
|
0.659
|
1.015
|
1.486
|
|
|
theta_hat
|
100
|
0
|
0.154
|
0.248
|
−0.318
|
0.129
|
1.411
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.523
|
0.771
|
−1.730
|
0.541
|
2.136
|
|
|
R2_demand
|
100
|
0
|
0.591
|
0.112
|
0.243
|
0.613
|
0.799
|
|
|
R2_supply
|
100
|
0
|
0.587
|
0.115
|
0.136
|
0.611
|
0.769
|
|
\(n = 200\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.030
|
0.447
|
8.912
|
9.959
|
11.050
|
|
|
alpha1_hat
|
100
|
0
|
0.800
|
6.976
|
−16.810
|
0.746
|
18.238
|
|
|
alpha2_hat
|
100
|
0
|
5.048
|
0.844
|
3.433
|
5.046
|
7.572
|
|
|
alpha3_hat
|
100
|
0
|
1.011
|
0.106
|
0.760
|
1.009
|
1.282
|
|
|
gamma0_hat
|
100
|
0
|
0.899
|
0.652
|
−0.767
|
0.956
|
2.249
|
|
|
gamma1_hat
|
100
|
0
|
1.289
|
7.650
|
−19.914
|
1.022
|
22.499
|
|
|
gamma2_hat
|
100
|
0
|
1.015
|
0.102
|
0.838
|
0.999
|
1.327
|
|
|
gamma3_hat
|
100
|
0
|
1.016
|
0.101
|
0.780
|
1.010
|
1.279
|
|
|
theta_hat
|
100
|
0
|
0.107
|
0.165
|
−0.308
|
0.107
|
0.583
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.615
|
0.968
|
−2.240
|
0.691
|
2.904
|
|
|
R2_demand
|
100
|
0
|
0.576
|
0.088
|
0.266
|
0.592
|
0.736
|
|
|
R2_supply
|
100
|
0
|
0.576
|
0.076
|
0.285
|
0.590
|
0.734
|
|
\(n = 1000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.000
|
0.183
|
9.653
|
9.977
|
10.385
|
|
|
alpha1_hat
|
100
|
0
|
1.291
|
2.956
|
−5.136
|
1.479
|
7.205
|
|
|
alpha2_hat
|
100
|
0
|
4.973
|
0.360
|
4.186
|
4.986
|
5.969
|
|
|
alpha3_hat
|
100
|
0
|
1.008
|
0.041
|
0.921
|
1.010
|
1.142
|
|
|
gamma0_hat
|
100
|
0
|
0.934
|
0.307
|
0.133
|
0.930
|
1.603
|
|
|
gamma1_hat
|
100
|
0
|
1.040
|
2.853
|
−6.274
|
0.913
|
6.886
|
|
|
gamma2_hat
|
100
|
0
|
1.008
|
0.047
|
0.881
|
1.004
|
1.116
|
|
|
gamma3_hat
|
100
|
0
|
1.008
|
0.041
|
0.923
|
1.013
|
1.109
|
|
|
theta_hat
|
100
|
0
|
0.107
|
0.067
|
−0.067
|
0.112
|
0.262
|
|
|
theta_hat_t_stats
|
100
|
0
|
1.503
|
0.905
|
−1.128
|
1.638
|
3.560
|
|
|
R2_demand
|
100
|
0
|
0.588
|
0.034
|
0.509
|
0.589
|
0.674
|
|
|
R2_supply
|
100
|
0
|
0.583
|
0.036
|
0.454
|
0.584
|
0.657
|
|
\(n = 2000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.985
|
0.133
|
9.706
|
9.966
|
10.504
|
|
|
alpha1_hat
|
100
|
0
|
0.858
|
2.075
|
−4.874
|
0.888
|
6.281
|
|
|
alpha2_hat
|
100
|
0
|
4.998
|
0.252
|
4.389
|
4.956
|
5.689
|
|
|
alpha3_hat
|
100
|
0
|
0.998
|
0.028
|
0.949
|
0.999
|
1.086
|
|
|
gamma0_hat
|
100
|
0
|
1.003
|
0.210
|
0.418
|
0.995
|
1.624
|
|
|
gamma1_hat
|
100
|
0
|
0.824
|
2.211
|
−4.046
|
0.848
|
6.384
|
|
|
gamma2_hat
|
100
|
0
|
0.999
|
0.030
|
0.925
|
1.001
|
1.076
|
|
|
gamma3_hat
|
100
|
0
|
1.003
|
0.038
|
0.910
|
1.004
|
1.096
|
|
|
theta_hat
|
100
|
0
|
0.104
|
0.054
|
−0.024
|
0.105
|
0.218
|
|
|
theta_hat_t_stats
|
100
|
0
|
2.106
|
1.054
|
−0.536
|
2.193
|
4.360
|
|
|
R2_demand
|
100
|
0
|
0.589
|
0.025
|
0.499
|
0.591
|
0.629
|
|
|
R2_supply
|
100
|
0
|
0.585
|
0.024
|
0.536
|
0.588
|
0.632
|
|
\(\alpha_2 =
20.0\)
\(n = 50\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.009
|
0.849
|
8.005
|
9.985
|
12.852
|
|
|
alpha1_hat
|
100
|
0
|
−1.334
|
57.303
|
−166.001
|
−4.268
|
170.300
|
|
|
alpha2_hat
|
100
|
0
|
20.221
|
6.912
|
0.669
|
19.854
|
41.702
|
|
|
alpha3_hat
|
100
|
0
|
0.983
|
0.197
|
0.505
|
0.978
|
1.448
|
|
|
gamma0_hat
|
100
|
0
|
0.537
|
2.043
|
−8.719
|
0.972
|
3.459
|
|
|
gamma1_hat
|
100
|
0
|
−24.302
|
161.538
|
−1481.399
|
−2.022
|
182.283
|
|
|
gamma2_hat
|
100
|
0
|
1.057
|
0.237
|
0.517
|
1.042
|
1.888
|
|
|
gamma3_hat
|
100
|
0
|
1.070
|
0.303
|
0.590
|
1.021
|
2.912
|
|
|
theta_hat
|
100
|
0
|
0.311
|
0.970
|
−0.520
|
0.131
|
8.392
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.371
|
0.953
|
−2.341
|
0.449
|
2.521
|
|
|
R2_demand
|
100
|
0
|
0.585
|
0.161
|
−0.060
|
0.619
|
0.858
|
|
|
R2_supply
|
100
|
0
|
0.551
|
0.385
|
−1.836
|
0.642
|
0.812
|
|
\(n = 100\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.136
|
0.644
|
8.713
|
10.140
|
11.647
|
|
|
alpha1_hat
|
100
|
0
|
−0.463
|
41.128
|
−102.521
|
0.213
|
130.323
|
|
|
alpha2_hat
|
100
|
0
|
20.640
|
4.822
|
8.791
|
20.220
|
31.189
|
|
|
alpha3_hat
|
100
|
0
|
1.009
|
0.145
|
0.699
|
1.004
|
1.313
|
|
|
gamma0_hat
|
100
|
0
|
0.813
|
1.015
|
−2.678
|
0.853
|
2.763
|
|
|
gamma1_hat
|
100
|
0
|
4.002
|
41.292
|
−96.370
|
7.400
|
91.148
|
|
|
gamma2_hat
|
100
|
0
|
1.025
|
0.163
|
0.713
|
1.016
|
1.521
|
|
|
gamma3_hat
|
100
|
0
|
1.011
|
0.142
|
0.715
|
1.001
|
1.375
|
|
|
theta_hat
|
100
|
0
|
0.098
|
0.220
|
−0.341
|
0.084
|
0.571
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.381
|
0.963
|
−1.942
|
0.392
|
2.439
|
|
|
R2_demand
|
100
|
0
|
0.563
|
0.146
|
0.035
|
0.586
|
0.793
|
|
|
R2_supply
|
100
|
0
|
0.593
|
0.111
|
0.091
|
0.594
|
0.809
|
|
\(n = 200\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.963
|
0.437
|
9.013
|
9.902
|
11.204
|
|
|
alpha1_hat
|
100
|
0
|
−3.256
|
26.239
|
−73.104
|
−0.447
|
61.611
|
|
|
alpha2_hat
|
100
|
0
|
20.285
|
3.231
|
13.759
|
20.306
|
30.019
|
|
|
alpha3_hat
|
100
|
0
|
0.998
|
0.111
|
0.765
|
0.996
|
1.329
|
|
|
gamma0_hat
|
100
|
0
|
0.929
|
0.673
|
−0.988
|
0.894
|
2.180
|
|
|
gamma1_hat
|
100
|
0
|
0.661
|
24.494
|
−77.505
|
−0.298
|
98.402
|
|
|
gamma2_hat
|
100
|
0
|
1.009
|
0.098
|
0.736
|
1.014
|
1.221
|
|
|
gamma3_hat
|
100
|
0
|
1.016
|
0.103
|
0.789
|
1.010
|
1.261
|
|
|
theta_hat
|
100
|
0
|
0.113
|
0.146
|
−0.378
|
0.121
|
0.502
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.671
|
0.910
|
−2.384
|
0.731
|
2.716
|
|
|
R2_demand
|
100
|
0
|
0.594
|
0.078
|
0.364
|
0.594
|
0.772
|
|
|
R2_supply
|
100
|
0
|
0.596
|
0.061
|
0.433
|
0.594
|
0.727
|
|
\(n = 1000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.995
|
0.207
|
9.460
|
10.015
|
10.476
|
|
|
alpha1_hat
|
100
|
0
|
0.251
|
10.457
|
−23.319
|
2.316
|
21.523
|
|
|
alpha2_hat
|
100
|
0
|
20.076
|
1.288
|
16.737
|
19.948
|
23.231
|
|
|
alpha3_hat
|
100
|
0
|
0.999
|
0.049
|
0.851
|
0.997
|
1.119
|
|
|
gamma0_hat
|
100
|
0
|
0.926
|
0.347
|
0.042
|
0.883
|
1.556
|
|
|
gamma1_hat
|
100
|
0
|
1.692
|
10.652
|
−19.769
|
1.393
|
33.092
|
|
|
gamma2_hat
|
100
|
0
|
1.011
|
0.049
|
0.918
|
1.004
|
1.140
|
|
|
gamma3_hat
|
100
|
0
|
1.013
|
0.043
|
0.903
|
1.013
|
1.136
|
|
|
theta_hat
|
100
|
0
|
0.104
|
0.063
|
−0.039
|
0.113
|
0.223
|
|
|
theta_hat_t_stats
|
100
|
0
|
1.505
|
0.888
|
−0.547
|
1.621
|
3.152
|
|
|
R2_demand
|
100
|
0
|
0.595
|
0.039
|
0.461
|
0.595
|
0.667
|
|
|
R2_supply
|
100
|
0
|
0.593
|
0.033
|
0.510
|
0.594
|
0.667
|
|
\(n = 2000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.992
|
0.142
|
9.640
|
9.988
|
10.326
|
|
|
alpha1_hat
|
100
|
0
|
0.453
|
8.219
|
−19.675
|
0.204
|
15.929
|
|
|
alpha2_hat
|
100
|
0
|
20.017
|
0.956
|
17.485
|
20.057
|
22.606
|
|
|
alpha3_hat
|
100
|
0
|
0.995
|
0.034
|
0.903
|
0.992
|
1.085
|
|
|
gamma0_hat
|
100
|
0
|
1.018
|
0.211
|
0.483
|
1.011
|
1.452
|
|
|
gamma1_hat
|
100
|
0
|
1.081
|
8.878
|
−18.857
|
−0.398
|
24.715
|
|
|
gamma2_hat
|
100
|
0
|
0.993
|
0.029
|
0.923
|
0.995
|
1.076
|
|
|
gamma3_hat
|
100
|
0
|
1.002
|
0.031
|
0.938
|
1.002
|
1.084
|
|
|
theta_hat
|
100
|
0
|
0.101
|
0.051
|
−0.045
|
0.098
|
0.224
|
|
|
theta_hat_t_stats
|
100
|
0
|
2.088
|
0.999
|
−0.978
|
2.101
|
4.154
|
|
|
R2_demand
|
100
|
0
|
0.597
|
0.026
|
0.518
|
0.600
|
0.642
|
|
|
R2_supply
|
100
|
0
|
0.593
|
0.026
|
0.533
|
0.592
|
0.655
|
|
\(\theta =
0.2\)
\(\alpha_2 =
0.1\)
\(n = 50\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.075
|
1.011
|
7.398
|
10.061
|
13.437
|
|
|
alpha1_hat
|
100
|
0
|
1.091
|
0.872
|
−0.569
|
1.004
|
5.993
|
|
|
alpha2_hat
|
100
|
0
|
0.095
|
0.088
|
−0.270
|
0.097
|
0.283
|
|
|
alpha3_hat
|
100
|
0
|
1.004
|
0.238
|
0.588
|
0.981
|
1.694
|
|
|
gamma0_hat
|
100
|
0
|
0.548
|
1.504
|
−4.717
|
0.941
|
3.049
|
|
|
gamma1_hat
|
100
|
0
|
2.574
|
22.776
|
−74.725
|
0.963
|
166.484
|
|
|
gamma2_hat
|
100
|
0
|
1.045
|
0.217
|
0.601
|
1.008
|
1.542
|
|
|
gamma3_hat
|
100
|
0
|
1.037
|
0.220
|
0.567
|
0.996
|
1.582
|
|
|
theta_hat
|
100
|
0
|
−0.708
|
13.455
|
−106.414
|
0.266
|
40.890
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.272
|
1.032
|
−2.096
|
0.262
|
2.472
|
|
|
R2_demand
|
100
|
0
|
0.229
|
0.389
|
−1.627
|
0.339
|
0.609
|
|
|
R2_supply
|
100
|
0
|
0.206
|
0.285
|
−0.901
|
0.305
|
0.694
|
|
\(n = 100\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.926
|
0.661
|
8.653
|
9.862
|
11.727
|
|
|
alpha1_hat
|
100
|
0
|
0.794
|
0.635
|
−0.550
|
0.785
|
2.855
|
|
|
alpha2_hat
|
100
|
0
|
0.117
|
0.064
|
−0.036
|
0.113
|
0.357
|
|
|
alpha3_hat
|
100
|
0
|
1.000
|
0.145
|
0.676
|
0.988
|
1.460
|
|
|
gamma0_hat
|
100
|
0
|
0.863
|
0.947
|
−1.332
|
1.010
|
2.758
|
|
|
gamma1_hat
|
100
|
0
|
0.879
|
2.071
|
−9.676
|
0.990
|
11.014
|
|
|
gamma2_hat
|
100
|
0
|
1.017
|
0.143
|
0.765
|
1.001
|
1.382
|
|
|
gamma3_hat
|
100
|
0
|
1.030
|
0.141
|
0.629
|
1.032
|
1.427
|
|
|
theta_hat
|
100
|
0
|
0.277
|
1.101
|
−5.315
|
0.223
|
5.698
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.385
|
0.951
|
−1.791
|
0.365
|
2.645
|
|
|
R2_demand
|
100
|
0
|
0.269
|
0.185
|
−0.489
|
0.302
|
0.527
|
|
|
R2_supply
|
100
|
0
|
0.265
|
0.180
|
−0.455
|
0.281
|
0.573
|
|
\(n = 200\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.959
|
0.434
|
8.882
|
9.918
|
11.708
|
|
|
alpha1_hat
|
100
|
0
|
0.941
|
0.458
|
−0.074
|
0.949
|
2.347
|
|
|
alpha2_hat
|
100
|
0
|
0.104
|
0.043
|
−0.022
|
0.102
|
0.237
|
|
|
alpha3_hat
|
100
|
0
|
1.001
|
0.102
|
0.755
|
0.998
|
1.358
|
|
|
gamma0_hat
|
100
|
0
|
0.948
|
0.712
|
−1.078
|
0.975
|
2.415
|
|
|
gamma1_hat
|
100
|
0
|
0.951
|
1.194
|
−2.037
|
1.051
|
7.303
|
|
|
gamma2_hat
|
100
|
0
|
1.005
|
0.112
|
0.712
|
1.001
|
1.284
|
|
|
gamma3_hat
|
100
|
0
|
1.007
|
0.102
|
0.747
|
1.012
|
1.239
|
|
|
theta_hat
|
100
|
0
|
0.256
|
0.636
|
−2.813
|
0.175
|
2.333
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.486
|
1.017
|
−2.527
|
0.456
|
2.639
|
|
|
R2_demand
|
100
|
0
|
0.264
|
0.137
|
−0.149
|
0.274
|
0.532
|
|
|
R2_supply
|
100
|
0
|
0.260
|
0.124
|
−0.197
|
0.272
|
0.466
|
|
\(n = 1000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.031
|
0.176
|
9.642
|
10.023
|
10.461
|
|
|
alpha1_hat
|
100
|
0
|
1.010
|
0.190
|
0.643
|
1.021
|
1.701
|
|
|
alpha2_hat
|
100
|
0
|
0.101
|
0.019
|
0.043
|
0.098
|
0.152
|
|
|
alpha3_hat
|
100
|
0
|
1.008
|
0.037
|
0.932
|
1.008
|
1.111
|
|
|
gamma0_hat
|
100
|
0
|
1.029
|
0.337
|
0.179
|
1.029
|
2.079
|
|
|
gamma1_hat
|
100
|
0
|
1.003
|
0.370
|
−0.138
|
1.008
|
1.761
|
|
|
gamma2_hat
|
100
|
0
|
0.993
|
0.051
|
0.846
|
0.990
|
1.116
|
|
|
gamma3_hat
|
100
|
0
|
0.995
|
0.046
|
0.880
|
0.995
|
1.112
|
|
|
theta_hat
|
100
|
0
|
0.196
|
0.191
|
−0.243
|
0.175
|
0.747
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.998
|
0.913
|
−1.285
|
1.012
|
3.137
|
|
|
R2_demand
|
100
|
0
|
0.264
|
0.056
|
0.134
|
0.271
|
0.373
|
|
|
R2_supply
|
100
|
0
|
0.272
|
0.050
|
0.111
|
0.273
|
0.364
|
|
\(n = 2000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.008
|
0.132
|
9.671
|
10.024
|
10.394
|
|
|
alpha1_hat
|
100
|
0
|
1.011
|
0.132
|
0.646
|
1.015
|
1.329
|
|
|
alpha2_hat
|
100
|
0
|
0.099
|
0.012
|
0.069
|
0.098
|
0.137
|
|
|
alpha3_hat
|
100
|
0
|
0.999
|
0.030
|
0.918
|
1.001
|
1.077
|
|
|
gamma0_hat
|
100
|
0
|
0.952
|
0.212
|
0.394
|
0.966
|
1.475
|
|
|
gamma1_hat
|
100
|
0
|
0.962
|
0.256
|
0.461
|
0.970
|
1.765
|
|
|
gamma2_hat
|
100
|
0
|
1.005
|
0.030
|
0.929
|
1.004
|
1.069
|
|
|
gamma3_hat
|
100
|
0
|
1.005
|
0.031
|
0.925
|
1.003
|
1.075
|
|
|
theta_hat
|
100
|
0
|
0.229
|
0.137
|
−0.166
|
0.216
|
0.521
|
|
|
theta_hat_t_stats
|
100
|
0
|
1.695
|
0.961
|
−1.275
|
1.658
|
3.443
|
|
|
R2_demand
|
100
|
0
|
0.276
|
0.042
|
0.161
|
0.276
|
0.375
|
|
|
R2_supply
|
100
|
0
|
0.269
|
0.037
|
0.170
|
0.273
|
0.362
|
|
\(\alpha_2 =
0.5\)
\(n = 50\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.931
|
0.852
|
7.610
|
9.913
|
12.363
|
|
|
alpha1_hat
|
100
|
0
|
0.945
|
2.071
|
−5.565
|
0.842
|
6.752
|
|
|
alpha2_hat
|
100
|
0
|
0.494
|
0.218
|
−0.055
|
0.491
|
1.175
|
|
|
alpha3_hat
|
100
|
0
|
0.991
|
0.212
|
0.508
|
0.965
|
1.470
|
|
|
gamma0_hat
|
100
|
0
|
0.902
|
1.615
|
−6.741
|
1.067
|
4.386
|
|
|
gamma1_hat
|
100
|
0
|
0.035
|
4.734
|
−35.358
|
0.795
|
6.217
|
|
|
gamma2_hat
|
100
|
0
|
0.995
|
0.212
|
0.588
|
0.980
|
1.714
|
|
|
gamma3_hat
|
100
|
0
|
0.989
|
0.210
|
0.510
|
0.993
|
1.529
|
|
|
theta_hat
|
100
|
0
|
0.415
|
0.873
|
−0.539
|
0.234
|
5.647
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.499
|
0.890
|
−1.713
|
0.593
|
2.092
|
|
|
R2_demand
|
100
|
0
|
0.366
|
0.272
|
−0.637
|
0.422
|
0.733
|
|
|
R2_supply
|
100
|
0
|
0.443
|
0.229
|
−0.644
|
0.481
|
0.799
|
|
\(n = 100\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.000
|
0.609
|
8.668
|
9.966
|
11.644
|
|
|
alpha1_hat
|
100
|
0
|
0.873
|
1.411
|
−2.676
|
0.841
|
4.144
|
|
|
alpha2_hat
|
100
|
0
|
0.514
|
0.145
|
0.207
|
0.512
|
1.042
|
|
|
alpha3_hat
|
100
|
0
|
1.013
|
0.139
|
0.662
|
1.010
|
1.360
|
|
|
gamma0_hat
|
100
|
0
|
0.886
|
1.115
|
−2.705
|
1.022
|
2.746
|
|
|
gamma1_hat
|
100
|
0
|
0.820
|
1.754
|
−4.287
|
0.737
|
5.277
|
|
|
gamma2_hat
|
100
|
0
|
1.015
|
0.163
|
0.761
|
0.999
|
1.562
|
|
|
gamma3_hat
|
100
|
0
|
1.008
|
0.169
|
0.710
|
0.971
|
1.518
|
|
|
theta_hat
|
100
|
0
|
0.249
|
0.361
|
−0.511
|
0.216
|
1.569
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.703
|
0.940
|
−1.470
|
0.733
|
3.272
|
|
|
R2_demand
|
100
|
0
|
0.411
|
0.176
|
−0.371
|
0.446
|
0.713
|
|
|
R2_supply
|
100
|
0
|
0.424
|
0.154
|
−0.248
|
0.446
|
0.663
|
|
\(n = 200\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.971
|
0.392
|
9.083
|
9.932
|
11.142
|
|
|
alpha1_hat
|
100
|
0
|
0.983
|
1.008
|
−1.916
|
1.021
|
3.446
|
|
|
alpha2_hat
|
100
|
0
|
0.498
|
0.106
|
0.255
|
0.489
|
0.800
|
|
|
alpha3_hat
|
100
|
0
|
0.983
|
0.095
|
0.814
|
0.981
|
1.286
|
|
|
gamma0_hat
|
100
|
0
|
0.755
|
0.696
|
−1.330
|
0.714
|
2.564
|
|
|
gamma1_hat
|
100
|
0
|
0.811
|
1.349
|
−2.427
|
0.846
|
4.138
|
|
|
gamma2_hat
|
100
|
0
|
1.028
|
0.098
|
0.814
|
1.018
|
1.310
|
|
|
gamma3_hat
|
100
|
0
|
1.031
|
0.095
|
0.803
|
1.030
|
1.332
|
|
|
theta_hat
|
100
|
0
|
0.273
|
0.238
|
−0.289
|
0.268
|
0.956
|
|
|
theta_hat_t_stats
|
100
|
0
|
1.127
|
0.927
|
−1.723
|
1.083
|
3.000
|
|
|
R2_demand
|
100
|
0
|
0.426
|
0.108
|
0.137
|
0.451
|
0.643
|
|
|
R2_supply
|
100
|
0
|
0.407
|
0.117
|
−0.046
|
0.403
|
0.639
|
|
\(n = 1000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.028
|
0.204
|
9.613
|
10.024
|
10.608
|
|
|
alpha1_hat
|
100
|
0
|
1.011
|
0.439
|
0.159
|
1.018
|
2.029
|
|
|
alpha2_hat
|
100
|
0
|
0.503
|
0.053
|
0.384
|
0.510
|
0.622
|
|
|
alpha3_hat
|
100
|
0
|
1.010
|
0.046
|
0.915
|
1.012
|
1.112
|
|
|
gamma0_hat
|
100
|
0
|
0.976
|
0.312
|
0.207
|
0.961
|
2.034
|
|
|
gamma1_hat
|
100
|
0
|
0.925
|
0.569
|
−0.508
|
0.882
|
2.970
|
|
|
gamma2_hat
|
100
|
0
|
1.002
|
0.047
|
0.860
|
1.003
|
1.134
|
|
|
gamma3_hat
|
100
|
0
|
1.003
|
0.042
|
0.882
|
1.001
|
1.118
|
|
|
theta_hat
|
100
|
0
|
0.215
|
0.110
|
−0.181
|
0.202
|
0.513
|
|
|
theta_hat_t_stats
|
100
|
0
|
2.230
|
1.047
|
−1.911
|
2.222
|
5.614
|
|
|
R2_demand
|
100
|
0
|
0.425
|
0.045
|
0.296
|
0.425
|
0.511
|
|
|
R2_supply
|
100
|
0
|
0.425
|
0.048
|
0.279
|
0.424
|
0.537
|
|
\(n = 2000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.001
|
0.135
|
9.705
|
9.999
|
10.503
|
|
|
alpha1_hat
|
100
|
0
|
1.015
|
0.304
|
0.296
|
1.053
|
1.931
|
|
|
alpha2_hat
|
100
|
0
|
0.499
|
0.031
|
0.434
|
0.495
|
0.592
|
|
|
alpha3_hat
|
100
|
0
|
1.002
|
0.030
|
0.923
|
1.002
|
1.124
|
|
|
gamma0_hat
|
100
|
0
|
0.988
|
0.211
|
0.491
|
1.000
|
1.475
|
|
|
gamma1_hat
|
100
|
0
|
0.940
|
0.370
|
0.050
|
0.914
|
1.805
|
|
|
gamma2_hat
|
100
|
0
|
1.000
|
0.030
|
0.932
|
0.998
|
1.068
|
|
|
gamma3_hat
|
100
|
0
|
1.001
|
0.030
|
0.912
|
1.002
|
1.077
|
|
|
theta_hat
|
100
|
0
|
0.213
|
0.065
|
0.038
|
0.224
|
0.324
|
|
|
theta_hat_t_stats
|
100
|
0
|
3.165
|
0.942
|
0.601
|
3.287
|
4.820
|
|
|
R2_demand
|
100
|
0
|
0.429
|
0.035
|
0.313
|
0.426
|
0.516
|
|
|
R2_supply
|
100
|
0
|
0.426
|
0.029
|
0.351
|
0.428
|
0.486
|
|
\(\alpha_2 =
1.0\)
\(n = 50\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.040
|
1.033
|
8.325
|
9.983
|
14.154
|
|
|
alpha1_hat
|
100
|
0
|
0.732
|
3.527
|
−7.984
|
0.989
|
13.497
|
|
|
alpha2_hat
|
100
|
0
|
1.034
|
0.395
|
−0.040
|
0.982
|
2.165
|
|
|
alpha3_hat
|
100
|
0
|
1.018
|
0.228
|
0.547
|
1.015
|
2.066
|
|
|
gamma0_hat
|
100
|
0
|
0.685
|
1.396
|
−3.283
|
0.908
|
3.717
|
|
|
gamma1_hat
|
100
|
0
|
−0.548
|
14.792
|
−137.315
|
1.171
|
18.350
|
|
|
gamma2_hat
|
100
|
0
|
1.035
|
0.209
|
0.596
|
1.011
|
1.701
|
|
|
gamma3_hat
|
100
|
0
|
1.052
|
0.237
|
0.534
|
1.020
|
1.689
|
|
|
theta_hat
|
100
|
0
|
0.374
|
1.192
|
−1.655
|
0.165
|
10.772
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.539
|
1.091
|
−2.646
|
0.446
|
3.378
|
|
|
R2_demand
|
100
|
0
|
0.442
|
0.271
|
−1.045
|
0.510
|
0.773
|
|
|
R2_supply
|
100
|
0
|
0.463
|
0.209
|
−0.202
|
0.503
|
0.849
|
|
\(n = 100\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.888
|
0.665
|
8.647
|
9.810
|
11.863
|
|
|
alpha1_hat
|
100
|
0
|
1.235
|
2.322
|
−4.598
|
1.410
|
5.977
|
|
|
alpha2_hat
|
100
|
0
|
0.950
|
0.277
|
0.235
|
0.969
|
1.804
|
|
|
alpha3_hat
|
100
|
0
|
0.979
|
0.162
|
0.634
|
0.967
|
1.363
|
|
|
gamma0_hat
|
100
|
0
|
0.991
|
0.985
|
−1.499
|
1.034
|
3.186
|
|
|
gamma1_hat
|
100
|
0
|
0.778
|
3.913
|
−17.340
|
1.335
|
8.883
|
|
|
gamma2_hat
|
100
|
0
|
0.993
|
0.143
|
0.652
|
0.984
|
1.396
|
|
|
gamma3_hat
|
100
|
0
|
1.015
|
0.159
|
0.660
|
0.995
|
1.431
|
|
|
theta_hat
|
100
|
0
|
0.246
|
0.429
|
−0.645
|
0.184
|
2.547
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.639
|
1.071
|
−1.637
|
0.676
|
3.217
|
|
|
R2_demand
|
100
|
0
|
0.474
|
0.143
|
−0.081
|
0.508
|
0.740
|
|
|
R2_supply
|
100
|
0
|
0.472
|
0.128
|
0.150
|
0.507
|
0.695
|
|
\(n = 200\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.989
|
0.402
|
9.067
|
9.978
|
10.821
|
|
|
alpha1_hat
|
100
|
0
|
0.892
|
1.662
|
−2.511
|
0.818
|
5.197
|
|
|
alpha2_hat
|
100
|
0
|
1.010
|
0.174
|
0.651
|
1.021
|
1.376
|
|
|
alpha3_hat
|
100
|
0
|
1.008
|
0.093
|
0.737
|
1.010
|
1.240
|
|
|
gamma0_hat
|
100
|
0
|
0.895
|
0.701
|
−1.357
|
0.977
|
2.249
|
|
|
gamma1_hat
|
100
|
0
|
1.147
|
1.722
|
−3.622
|
1.101
|
5.098
|
|
|
gamma2_hat
|
100
|
0
|
1.018
|
0.107
|
0.777
|
1.008
|
1.352
|
|
|
gamma3_hat
|
100
|
0
|
1.013
|
0.098
|
0.841
|
1.005
|
1.347
|
|
|
theta_hat
|
100
|
0
|
0.198
|
0.183
|
−0.195
|
0.210
|
0.722
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.970
|
0.895
|
−0.912
|
1.048
|
2.782
|
|
|
R2_demand
|
100
|
0
|
0.475
|
0.105
|
0.002
|
0.487
|
0.678
|
|
|
R2_supply
|
100
|
0
|
0.467
|
0.099
|
0.056
|
0.481
|
0.651
|
|
\(n = 1000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.988
|
0.171
|
9.578
|
9.975
|
10.431
|
|
|
alpha1_hat
|
100
|
0
|
0.821
|
0.715
|
−0.816
|
0.789
|
2.254
|
|
|
alpha2_hat
|
100
|
0
|
1.015
|
0.078
|
0.850
|
1.014
|
1.272
|
|
|
alpha3_hat
|
100
|
0
|
0.997
|
0.042
|
0.893
|
1.000
|
1.083
|
|
|
gamma0_hat
|
100
|
0
|
0.963
|
0.309
|
0.199
|
0.954
|
1.754
|
|
|
gamma1_hat
|
100
|
0
|
1.064
|
0.759
|
−0.706
|
1.039
|
3.020
|
|
|
gamma2_hat
|
100
|
0
|
1.004
|
0.045
|
0.875
|
1.004
|
1.105
|
|
|
gamma3_hat
|
100
|
0
|
1.003
|
0.044
|
0.893
|
1.005
|
1.115
|
|
|
theta_hat
|
100
|
0
|
0.201
|
0.078
|
0.025
|
0.204
|
0.366
|
|
|
theta_hat_t_stats
|
100
|
0
|
2.413
|
0.878
|
0.311
|
2.459
|
4.222
|
|
|
R2_demand
|
100
|
0
|
0.473
|
0.043
|
0.342
|
0.479
|
0.554
|
|
|
R2_supply
|
100
|
0
|
0.470
|
0.043
|
0.356
|
0.470
|
0.578
|
|
\(n = 2000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.996
|
0.145
|
9.645
|
9.980
|
10.376
|
|
|
alpha1_hat
|
100
|
0
|
1.038
|
0.491
|
0.048
|
1.017
|
2.282
|
|
|
alpha2_hat
|
100
|
0
|
0.995
|
0.058
|
0.795
|
0.986
|
1.122
|
|
|
alpha3_hat
|
100
|
0
|
1.000
|
0.032
|
0.908
|
1.001
|
1.091
|
|
|
gamma0_hat
|
100
|
0
|
0.962
|
0.217
|
0.315
|
0.979
|
1.463
|
|
|
gamma1_hat
|
100
|
0
|
1.026
|
0.641
|
−0.504
|
1.069
|
2.565
|
|
|
gamma2_hat
|
100
|
0
|
1.004
|
0.034
|
0.933
|
1.000
|
1.087
|
|
|
gamma3_hat
|
100
|
0
|
1.001
|
0.031
|
0.910
|
1.003
|
1.110
|
|
|
theta_hat
|
100
|
0
|
0.204
|
0.064
|
0.042
|
0.199
|
0.377
|
|
|
theta_hat_t_stats
|
100
|
0
|
3.397
|
0.972
|
0.804
|
3.354
|
5.773
|
|
|
R2_demand
|
100
|
0
|
0.479
|
0.035
|
0.380
|
0.483
|
0.534
|
|
|
R2_supply
|
100
|
0
|
0.472
|
0.028
|
0.404
|
0.472
|
0.545
|
|
\(\alpha_2 =
5.0\)
\(n = 50\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.002
|
1.058
|
7.983
|
9.898
|
14.800
|
|
|
alpha1_hat
|
100
|
0
|
1.377
|
15.017
|
−48.230
|
0.894
|
38.341
|
|
|
alpha2_hat
|
100
|
0
|
4.940
|
1.918
|
0.544
|
4.849
|
15.191
|
|
|
alpha3_hat
|
100
|
0
|
1.006
|
0.242
|
0.572
|
0.991
|
2.311
|
|
|
gamma0_hat
|
100
|
0
|
0.511
|
1.736
|
−5.222
|
0.866
|
3.351
|
|
|
gamma1_hat
|
100
|
0
|
−4.801
|
27.217
|
−157.492
|
1.365
|
32.063
|
|
|
gamma2_hat
|
100
|
0
|
1.067
|
0.272
|
0.558
|
1.023
|
2.006
|
|
|
gamma3_hat
|
100
|
0
|
1.058
|
0.206
|
0.657
|
1.021
|
1.673
|
|
|
theta_hat
|
100
|
0
|
0.391
|
0.651
|
−0.854
|
0.264
|
3.853
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.655
|
0.933
|
−3.120
|
0.694
|
2.744
|
|
|
R2_demand
|
100
|
0
|
0.506
|
0.292
|
−1.126
|
0.570
|
0.816
|
|
|
R2_supply
|
100
|
0
|
0.493
|
0.231
|
−0.546
|
0.550
|
0.794
|
|
\(n = 100\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.019
|
0.671
|
8.679
|
10.062
|
12.231
|
|
|
alpha1_hat
|
100
|
0
|
2.664
|
10.353
|
−18.538
|
1.161
|
33.037
|
|
|
alpha2_hat
|
100
|
0
|
4.837
|
1.178
|
1.936
|
4.857
|
7.383
|
|
|
alpha3_hat
|
100
|
0
|
1.002
|
0.139
|
0.698
|
0.996
|
1.357
|
|
|
gamma0_hat
|
100
|
0
|
0.999
|
0.967
|
−1.678
|
1.054
|
3.016
|
|
|
gamma1_hat
|
100
|
0
|
−0.080
|
11.572
|
−49.144
|
0.659
|
23.910
|
|
|
gamma2_hat
|
100
|
0
|
0.993
|
0.160
|
0.569
|
0.981
|
1.481
|
|
|
gamma3_hat
|
100
|
0
|
0.997
|
0.155
|
0.681
|
0.995
|
1.343
|
|
|
theta_hat
|
100
|
0
|
0.235
|
0.280
|
−0.298
|
0.192
|
1.542
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.775
|
0.816
|
−1.355
|
0.739
|
2.769
|
|
|
R2_demand
|
100
|
0
|
0.507
|
0.151
|
−0.049
|
0.532
|
0.741
|
|
|
R2_supply
|
100
|
0
|
0.530
|
0.121
|
0.133
|
0.545
|
0.762
|
|
\(n = 200\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.955
|
0.387
|
9.235
|
9.913
|
11.116
|
|
|
alpha1_hat
|
100
|
0
|
0.953
|
6.612
|
−20.606
|
1.011
|
18.557
|
|
|
alpha2_hat
|
100
|
0
|
4.949
|
0.771
|
3.250
|
4.930
|
7.343
|
|
|
alpha3_hat
|
100
|
0
|
0.980
|
0.087
|
0.739
|
0.973
|
1.348
|
|
|
gamma0_hat
|
100
|
0
|
0.897
|
0.786
|
−1.441
|
1.018
|
2.274
|
|
|
gamma1_hat
|
100
|
0
|
0.073
|
7.274
|
−23.077
|
0.463
|
18.307
|
|
|
gamma2_hat
|
100
|
0
|
1.013
|
0.114
|
0.813
|
0.995
|
1.324
|
|
|
gamma3_hat
|
100
|
0
|
1.007
|
0.110
|
0.743
|
1.009
|
1.265
|
|
|
theta_hat
|
100
|
0
|
0.238
|
0.176
|
−0.171
|
0.218
|
0.814
|
|
|
theta_hat_t_stats
|
100
|
0
|
1.266
|
0.860
|
−1.171
|
1.262
|
2.948
|
|
|
R2_demand
|
100
|
0
|
0.521
|
0.102
|
0.148
|
0.532
|
0.682
|
|
|
R2_supply
|
100
|
0
|
0.505
|
0.101
|
0.201
|
0.524
|
0.676
|
|
\(n = 1000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.982
|
0.193
|
9.560
|
9.971
|
10.435
|
|
|
alpha1_hat
|
100
|
0
|
1.092
|
3.330
|
−6.629
|
0.974
|
7.706
|
|
|
alpha2_hat
|
100
|
0
|
4.972
|
0.378
|
4.148
|
5.007
|
5.920
|
|
|
alpha3_hat
|
100
|
0
|
0.992
|
0.049
|
0.891
|
0.986
|
1.130
|
|
|
gamma0_hat
|
100
|
0
|
0.945
|
0.330
|
−0.030
|
0.942
|
1.641
|
|
|
gamma1_hat
|
100
|
0
|
0.908
|
3.676
|
−7.279
|
0.801
|
10.889
|
|
|
gamma2_hat
|
100
|
0
|
1.006
|
0.047
|
0.896
|
1.008
|
1.126
|
|
|
gamma3_hat
|
100
|
0
|
1.013
|
0.047
|
0.900
|
1.010
|
1.109
|
|
|
theta_hat
|
100
|
0
|
0.211
|
0.078
|
0.001
|
0.211
|
0.369
|
|
|
theta_hat_t_stats
|
100
|
0
|
2.746
|
0.945
|
0.017
|
2.874
|
4.744
|
|
|
R2_demand
|
100
|
0
|
0.521
|
0.039
|
0.432
|
0.517
|
0.609
|
|
|
R2_supply
|
100
|
0
|
0.517
|
0.039
|
0.408
|
0.522
|
0.604
|
|
\(n = 2000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.999
|
0.134
|
9.692
|
10.002
|
10.278
|
|
|
alpha1_hat
|
100
|
0
|
1.050
|
2.303
|
−6.558
|
1.026
|
6.791
|
|
|
alpha2_hat
|
100
|
0
|
4.995
|
0.248
|
4.188
|
4.964
|
5.820
|
|
|
alpha3_hat
|
100
|
0
|
1.002
|
0.030
|
0.929
|
1.001
|
1.072
|
|
|
gamma0_hat
|
100
|
0
|
0.983
|
0.216
|
0.423
|
0.979
|
1.454
|
|
|
gamma1_hat
|
100
|
0
|
0.878
|
2.265
|
−4.816
|
0.770
|
6.018
|
|
|
gamma2_hat
|
100
|
0
|
1.003
|
0.033
|
0.915
|
1.000
|
1.104
|
|
|
gamma3_hat
|
100
|
0
|
0.995
|
0.031
|
0.916
|
1.001
|
1.074
|
|
|
theta_hat
|
100
|
0
|
0.205
|
0.052
|
0.093
|
0.209
|
0.337
|
|
|
theta_hat_t_stats
|
100
|
0
|
3.838
|
0.892
|
1.855
|
3.918
|
6.058
|
|
|
R2_demand
|
100
|
0
|
0.519
|
0.029
|
0.437
|
0.521
|
0.587
|
|
|
R2_supply
|
100
|
0
|
0.517
|
0.027
|
0.437
|
0.514
|
0.566
|
|
\(\alpha_2 =
20.0\)
\(n = 50\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.907
|
0.938
|
7.866
|
9.809
|
12.850
|
|
|
alpha1_hat
|
100
|
0
|
1.370
|
51.562
|
−120.993
|
−5.489
|
170.972
|
|
|
alpha2_hat
|
100
|
0
|
19.581
|
6.126
|
3.832
|
19.461
|
40.350
|
|
|
alpha3_hat
|
100
|
0
|
0.994
|
0.232
|
0.524
|
0.955
|
1.846
|
|
|
gamma0_hat
|
100
|
0
|
0.408
|
2.155
|
−9.663
|
0.710
|
4.317
|
|
|
gamma1_hat
|
100
|
0
|
6.310
|
89.940
|
−415.311
|
10.375
|
192.299
|
|
|
gamma2_hat
|
100
|
0
|
1.058
|
0.282
|
0.548
|
1.047
|
2.227
|
|
|
gamma3_hat
|
100
|
0
|
1.080
|
0.347
|
0.632
|
1.011
|
2.963
|
|
|
theta_hat
|
100
|
0
|
0.262
|
0.494
|
−0.626
|
0.172
|
2.440
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.423
|
0.913
|
−2.026
|
0.516
|
2.709
|
|
|
R2_demand
|
100
|
0
|
0.504
|
0.230
|
−0.385
|
0.553
|
0.813
|
|
|
R2_supply
|
100
|
0
|
0.451
|
0.365
|
−2.320
|
0.541
|
0.816
|
|
\(n = 100\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.964
|
0.590
|
8.849
|
9.864
|
12.076
|
|
|
alpha1_hat
|
100
|
0
|
−6.842
|
38.993
|
−106.509
|
−8.018
|
94.391
|
|
|
alpha2_hat
|
100
|
0
|
20.716
|
4.666
|
11.087
|
20.285
|
34.440
|
|
|
alpha3_hat
|
100
|
0
|
0.994
|
0.129
|
0.703
|
0.993
|
1.496
|
|
|
gamma0_hat
|
100
|
0
|
1.017
|
1.082
|
−2.746
|
1.186
|
2.885
|
|
|
gamma1_hat
|
100
|
0
|
−0.088
|
44.747
|
−150.445
|
1.305
|
160.906
|
|
|
gamma2_hat
|
100
|
0
|
1.003
|
0.161
|
0.668
|
0.977
|
1.508
|
|
|
gamma3_hat
|
100
|
0
|
0.978
|
0.148
|
0.646
|
0.972
|
1.490
|
|
|
theta_hat
|
100
|
0
|
0.206
|
0.265
|
−0.593
|
0.154
|
1.063
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.767
|
0.882
|
−1.602
|
0.700
|
2.806
|
|
|
R2_demand
|
100
|
0
|
0.526
|
0.168
|
−0.418
|
0.558
|
0.786
|
|
|
R2_supply
|
100
|
0
|
0.546
|
0.115
|
0.195
|
0.570
|
0.718
|
|
\(n = 200\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.041
|
0.450
|
9.145
|
10.047
|
11.300
|
|
|
alpha1_hat
|
100
|
0
|
3.898
|
32.444
|
−76.175
|
2.590
|
80.157
|
|
|
alpha2_hat
|
100
|
0
|
19.927
|
3.680
|
12.924
|
19.748
|
32.442
|
|
|
alpha3_hat
|
100
|
0
|
1.025
|
0.102
|
0.792
|
1.028
|
1.270
|
|
|
gamma0_hat
|
100
|
0
|
1.040
|
0.623
|
−0.460
|
1.052
|
2.627
|
|
|
gamma1_hat
|
100
|
0
|
−4.063
|
25.418
|
−65.590
|
−4.101
|
47.477
|
|
|
gamma2_hat
|
100
|
0
|
0.990
|
0.095
|
0.707
|
0.983
|
1.242
|
|
|
gamma3_hat
|
100
|
0
|
1.003
|
0.099
|
0.771
|
0.997
|
1.234
|
|
|
theta_hat
|
100
|
0
|
0.222
|
0.151
|
−0.115
|
0.210
|
0.605
|
|
|
theta_hat_t_stats
|
100
|
0
|
1.242
|
0.758
|
−0.918
|
1.286
|
2.638
|
|
|
R2_demand
|
100
|
0
|
0.517
|
0.094
|
0.251
|
0.529
|
0.722
|
|
|
R2_supply
|
100
|
0
|
0.523
|
0.085
|
0.209
|
0.541
|
0.655
|
|
\(n = 1000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.986
|
0.172
|
9.642
|
9.959
|
10.463
|
|
|
alpha1_hat
|
100
|
0
|
1.846
|
13.554
|
−32.313
|
1.997
|
35.088
|
|
|
alpha2_hat
|
100
|
0
|
19.849
|
1.481
|
16.789
|
19.801
|
23.422
|
|
|
alpha3_hat
|
100
|
0
|
0.995
|
0.044
|
0.904
|
0.992
|
1.124
|
|
|
gamma0_hat
|
100
|
0
|
1.037
|
0.276
|
0.146
|
1.034
|
1.619
|
|
|
gamma1_hat
|
100
|
0
|
−0.142
|
13.378
|
−30.588
|
−1.968
|
38.986
|
|
|
gamma2_hat
|
100
|
0
|
0.997
|
0.040
|
0.914
|
0.993
|
1.104
|
|
|
gamma3_hat
|
100
|
0
|
0.998
|
0.046
|
0.907
|
0.993
|
1.134
|
|
|
theta_hat
|
100
|
0
|
0.202
|
0.076
|
0.026
|
0.211
|
0.375
|
|
|
theta_hat_t_stats
|
100
|
0
|
2.699
|
0.965
|
0.373
|
2.843
|
5.085
|
|
|
R2_demand
|
100
|
0
|
0.531
|
0.041
|
0.385
|
0.536
|
0.609
|
|
|
R2_supply
|
100
|
0
|
0.534
|
0.033
|
0.431
|
0.534
|
0.645
|
|
\(n = 2000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.989
|
0.154
|
9.663
|
9.990
|
10.370
|
|
|
alpha1_hat
|
100
|
0
|
2.484
|
8.549
|
−26.399
|
3.687
|
21.425
|
|
|
alpha2_hat
|
100
|
0
|
19.802
|
1.119
|
17.548
|
19.748
|
23.647
|
|
|
alpha3_hat
|
100
|
0
|
0.999
|
0.034
|
0.918
|
1.000
|
1.075
|
|
|
gamma0_hat
|
100
|
0
|
0.989
|
0.192
|
0.541
|
0.985
|
1.465
|
|
|
gamma1_hat
|
100
|
0
|
1.404
|
9.574
|
−24.190
|
1.093
|
20.914
|
|
|
gamma2_hat
|
100
|
0
|
1.003
|
0.029
|
0.919
|
1.002
|
1.087
|
|
|
gamma3_hat
|
100
|
0
|
0.998
|
0.031
|
0.928
|
1.000
|
1.061
|
|
|
theta_hat
|
100
|
0
|
0.199
|
0.053
|
0.077
|
0.196
|
0.329
|
|
|
theta_hat_t_stats
|
100
|
0
|
3.772
|
0.896
|
1.580
|
3.739
|
5.662
|
|
|
R2_demand
|
100
|
0
|
0.530
|
0.029
|
0.470
|
0.531
|
0.594
|
|
|
R2_supply
|
100
|
0
|
0.527
|
0.024
|
0.466
|
0.527
|
0.599
|
|
\(\theta =
0.33\)
\(\alpha_2 =
0.1\)
\(n = 50\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.101
|
0.903
|
7.916
|
10.022
|
12.702
|
|
|
alpha1_hat
|
100
|
0
|
1.053
|
1.063
|
−1.100
|
0.896
|
4.684
|
|
|
alpha2_hat
|
100
|
0
|
0.102
|
0.093
|
−0.171
|
0.098
|
0.323
|
|
|
alpha3_hat
|
100
|
0
|
1.003
|
0.219
|
0.569
|
0.991
|
1.623
|
|
|
gamma0_hat
|
100
|
0
|
1.065
|
1.516
|
−4.142
|
1.438
|
4.185
|
|
|
gamma1_hat
|
100
|
0
|
4.401
|
33.922
|
−15.564
|
1.224
|
337.594
|
|
|
gamma2_hat
|
100
|
0
|
0.982
|
0.211
|
0.382
|
0.949
|
1.643
|
|
|
gamma3_hat
|
100
|
0
|
0.981
|
0.200
|
0.535
|
0.958
|
1.596
|
|
|
theta_hat
|
100
|
0
|
−1.026
|
13.210
|
−129.878
|
0.127
|
9.248
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.150
|
0.935
|
−2.170
|
0.180
|
2.524
|
|
|
R2_demand
|
100
|
0
|
0.169
|
0.305
|
−0.935
|
0.247
|
0.609
|
|
|
R2_supply
|
100
|
0
|
0.233
|
0.276
|
−0.713
|
0.264
|
0.733
|
|
\(n = 100\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.942
|
0.645
|
8.511
|
9.888
|
11.803
|
|
|
alpha1_hat
|
100
|
0
|
1.035
|
0.659
|
−1.098
|
1.009
|
2.949
|
|
|
alpha2_hat
|
100
|
0
|
0.094
|
0.060
|
−0.039
|
0.092
|
0.305
|
|
|
alpha3_hat
|
100
|
0
|
1.003
|
0.158
|
0.666
|
0.989
|
1.558
|
|
|
gamma0_hat
|
100
|
0
|
1.035
|
1.136
|
−2.674
|
1.152
|
2.769
|
|
|
gamma1_hat
|
100
|
0
|
1.637
|
6.820
|
−14.264
|
0.813
|
52.629
|
|
|
gamma2_hat
|
100
|
0
|
0.995
|
0.166
|
0.703
|
0.966
|
1.457
|
|
|
gamma3_hat
|
100
|
0
|
0.999
|
0.160
|
0.665
|
0.985
|
1.541
|
|
|
theta_hat
|
100
|
0
|
−0.004
|
3.435
|
−26.394
|
0.403
|
8.146
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.438
|
0.969
|
−1.833
|
0.528
|
2.155
|
|
|
R2_demand
|
100
|
0
|
0.245
|
0.153
|
−0.357
|
0.283
|
0.542
|
|
|
R2_supply
|
100
|
0
|
0.242
|
0.197
|
−0.353
|
0.277
|
0.604
|
|
\(n = 200\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.021
|
0.418
|
9.172
|
9.970
|
11.266
|
|
|
alpha1_hat
|
100
|
0
|
1.039
|
0.462
|
−0.247
|
0.990
|
2.050
|
|
|
alpha2_hat
|
100
|
0
|
0.097
|
0.042
|
−0.003
|
0.096
|
0.235
|
|
|
alpha3_hat
|
100
|
0
|
1.008
|
0.096
|
0.801
|
1.004
|
1.253
|
|
|
gamma0_hat
|
100
|
0
|
0.854
|
0.652
|
−0.964
|
0.852
|
2.344
|
|
|
gamma1_hat
|
100
|
0
|
0.661
|
1.543
|
−11.142
|
0.899
|
4.071
|
|
|
gamma2_hat
|
100
|
0
|
1.014
|
0.094
|
0.837
|
1.006
|
1.252
|
|
|
gamma3_hat
|
100
|
0
|
1.026
|
0.101
|
0.817
|
1.024
|
1.278
|
|
|
theta_hat
|
100
|
0
|
0.529
|
0.745
|
−0.976
|
0.379
|
6.205
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.911
|
0.748
|
−0.853
|
0.832
|
2.497
|
|
|
R2_demand
|
100
|
0
|
0.230
|
0.134
|
−0.151
|
0.238
|
0.537
|
|
|
R2_supply
|
100
|
0
|
0.211
|
0.145
|
−0.245
|
0.219
|
0.473
|
|
\(n = 1000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.987
|
0.203
|
9.377
|
9.972
|
10.663
|
|
|
alpha1_hat
|
100
|
0
|
1.005
|
0.200
|
0.332
|
1.003
|
1.444
|
|
|
alpha2_hat
|
100
|
0
|
0.099
|
0.020
|
0.053
|
0.101
|
0.155
|
|
|
alpha3_hat
|
100
|
0
|
1.004
|
0.048
|
0.843
|
1.004
|
1.118
|
|
|
gamma0_hat
|
100
|
0
|
1.011
|
0.300
|
0.171
|
1.027
|
1.736
|
|
|
gamma1_hat
|
100
|
0
|
0.959
|
0.411
|
−0.356
|
0.954
|
1.920
|
|
|
gamma2_hat
|
100
|
0
|
0.995
|
0.050
|
0.861
|
0.996
|
1.121
|
|
|
gamma3_hat
|
100
|
0
|
1.008
|
0.038
|
0.926
|
1.003
|
1.103
|
|
|
theta_hat
|
100
|
0
|
0.355
|
0.213
|
−0.201
|
0.351
|
1.184
|
|
|
theta_hat_t_stats
|
100
|
0
|
1.713
|
0.967
|
−1.073
|
1.808
|
4.122
|
|
|
R2_demand
|
100
|
0
|
0.241
|
0.058
|
0.101
|
0.249
|
0.371
|
|
|
R2_supply
|
100
|
0
|
0.237
|
0.061
|
0.116
|
0.239
|
0.366
|
|
\(n = 2000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.010
|
0.136
|
9.632
|
10.018
|
10.284
|
|
|
alpha1_hat
|
100
|
0
|
1.010
|
0.130
|
0.719
|
1.001
|
1.343
|
|
|
alpha2_hat
|
100
|
0
|
0.099
|
0.014
|
0.067
|
0.098
|
0.142
|
|
|
alpha3_hat
|
100
|
0
|
0.998
|
0.033
|
0.931
|
0.999
|
1.087
|
|
|
gamma0_hat
|
100
|
0
|
1.007
|
0.192
|
0.438
|
1.037
|
1.375
|
|
|
gamma1_hat
|
100
|
0
|
0.948
|
0.311
|
0.071
|
0.921
|
1.874
|
|
|
gamma2_hat
|
100
|
0
|
0.998
|
0.031
|
0.924
|
0.998
|
1.103
|
|
|
gamma3_hat
|
100
|
0
|
0.998
|
0.027
|
0.943
|
0.998
|
1.076
|
|
|
theta_hat
|
100
|
0
|
0.354
|
0.156
|
−0.140
|
0.352
|
0.801
|
|
|
theta_hat_t_stats
|
100
|
0
|
2.481
|
1.054
|
−1.044
|
2.525
|
4.915
|
|
|
R2_demand
|
100
|
0
|
0.230
|
0.042
|
0.126
|
0.223
|
0.333
|
|
|
R2_supply
|
100
|
0
|
0.237
|
0.039
|
0.152
|
0.235
|
0.331
|
|
\(\alpha_2 =
0.5\)
\(n = 50\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.788
|
0.869
|
7.639
|
9.751
|
13.200
|
|
|
alpha1_hat
|
100
|
0
|
0.846
|
2.077
|
−3.651
|
0.938
|
6.905
|
|
|
alpha2_hat
|
100
|
0
|
0.484
|
0.233
|
−0.058
|
0.490
|
1.293
|
|
|
alpha3_hat
|
100
|
0
|
0.971
|
0.219
|
0.492
|
0.951
|
1.737
|
|
|
gamma0_hat
|
100
|
0
|
1.061
|
1.365
|
−2.315
|
1.101
|
4.408
|
|
|
gamma1_hat
|
100
|
0
|
0.042
|
22.643
|
−146.792
|
1.182
|
118.213
|
|
|
gamma2_hat
|
100
|
0
|
1.002
|
0.196
|
0.603
|
0.988
|
1.425
|
|
|
gamma3_hat
|
100
|
0
|
0.992
|
0.190
|
0.624
|
0.982
|
1.567
|
|
|
theta_hat
|
100
|
0
|
0.513
|
4.245
|
−17.446
|
0.260
|
27.957
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.510
|
0.974
|
−3.851
|
0.583
|
2.632
|
|
|
R2_demand
|
100
|
0
|
0.366
|
0.273
|
−1.213
|
0.436
|
0.762
|
|
|
R2_supply
|
100
|
0
|
0.367
|
0.246
|
−0.378
|
0.424
|
0.800
|
|
\(n = 100\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.124
|
0.601
|
8.625
|
10.097
|
11.521
|
|
|
alpha1_hat
|
100
|
0
|
0.972
|
1.435
|
−3.407
|
0.881
|
5.203
|
|
|
alpha2_hat
|
100
|
0
|
0.523
|
0.162
|
0.116
|
0.529
|
0.973
|
|
|
alpha3_hat
|
100
|
0
|
1.044
|
0.148
|
0.716
|
1.051
|
1.519
|
|
|
gamma0_hat
|
100
|
0
|
1.200
|
0.851
|
−0.579
|
1.262
|
3.107
|
|
|
gamma1_hat
|
100
|
0
|
1.052
|
1.975
|
−4.719
|
1.070
|
7.520
|
|
|
gamma2_hat
|
100
|
0
|
0.985
|
0.126
|
0.697
|
0.989
|
1.263
|
|
|
gamma3_hat
|
100
|
0
|
0.976
|
0.136
|
0.557
|
0.973
|
1.354
|
|
|
theta_hat
|
100
|
0
|
0.282
|
0.345
|
−0.644
|
0.258
|
1.505
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.783
|
0.806
|
−1.187
|
0.956
|
2.203
|
|
|
R2_demand
|
100
|
0
|
0.314
|
0.194
|
−0.334
|
0.351
|
0.618
|
|
|
R2_supply
|
100
|
0
|
0.409
|
0.142
|
−0.110
|
0.432
|
0.686
|
|
\(n = 200\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.969
|
0.451
|
8.923
|
9.933
|
11.168
|
|
|
alpha1_hat
|
100
|
0
|
0.994
|
1.062
|
−2.433
|
0.846
|
4.063
|
|
|
alpha2_hat
|
100
|
0
|
0.496
|
0.109
|
0.221
|
0.488
|
0.786
|
|
|
alpha3_hat
|
100
|
0
|
0.999
|
0.116
|
0.726
|
1.009
|
1.273
|
|
|
gamma0_hat
|
100
|
0
|
1.154
|
0.607
|
−0.438
|
1.157
|
2.422
|
|
|
gamma1_hat
|
100
|
0
|
0.901
|
1.635
|
−3.139
|
0.952
|
4.285
|
|
|
gamma2_hat
|
100
|
0
|
0.979
|
0.087
|
0.767
|
0.975
|
1.239
|
|
|
gamma3_hat
|
100
|
0
|
0.997
|
0.105
|
0.723
|
0.989
|
1.348
|
|
|
theta_hat
|
100
|
0
|
0.329
|
0.285
|
−0.214
|
0.290
|
1.076
|
|
|
theta_hat_t_stats
|
100
|
0
|
1.306
|
1.048
|
−0.894
|
1.256
|
3.955
|
|
|
R2_demand
|
100
|
0
|
0.357
|
0.115
|
0.000
|
0.379
|
0.556
|
|
|
R2_supply
|
100
|
0
|
0.374
|
0.112
|
0.096
|
0.382
|
0.596
|
|
\(n = 1000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.989
|
0.216
|
9.527
|
9.985
|
10.570
|
|
|
alpha1_hat
|
100
|
0
|
0.921
|
0.428
|
−0.146
|
0.935
|
2.314
|
|
|
alpha2_hat
|
100
|
0
|
0.506
|
0.054
|
0.332
|
0.504
|
0.620
|
|
|
alpha3_hat
|
100
|
0
|
1.000
|
0.042
|
0.899
|
1.000
|
1.119
|
|
|
gamma0_hat
|
100
|
0
|
1.017
|
0.287
|
−0.045
|
1.054
|
1.589
|
|
|
gamma1_hat
|
100
|
0
|
1.098
|
0.555
|
−0.208
|
1.035
|
2.450
|
|
|
gamma2_hat
|
100
|
0
|
1.000
|
0.042
|
0.899
|
1.005
|
1.117
|
|
|
gamma3_hat
|
100
|
0
|
1.000
|
0.043
|
0.897
|
0.994
|
1.095
|
|
|
theta_hat
|
100
|
0
|
0.311
|
0.105
|
0.044
|
0.306
|
0.590
|
|
|
theta_hat_t_stats
|
100
|
0
|
3.020
|
0.907
|
0.415
|
3.118
|
4.864
|
|
|
R2_demand
|
100
|
0
|
0.355
|
0.058
|
0.160
|
0.364
|
0.475
|
|
|
R2_supply
|
100
|
0
|
0.365
|
0.045
|
0.234
|
0.363
|
0.469
|
|
\(n = 2000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.983
|
0.126
|
9.699
|
9.986
|
10.273
|
|
|
alpha1_hat
|
100
|
0
|
0.951
|
0.318
|
0.161
|
0.927
|
1.761
|
|
|
alpha2_hat
|
100
|
0
|
0.503
|
0.034
|
0.427
|
0.500
|
0.587
|
|
|
alpha3_hat
|
100
|
0
|
0.996
|
0.031
|
0.916
|
0.995
|
1.082
|
|
|
gamma0_hat
|
100
|
0
|
0.978
|
0.216
|
0.407
|
0.992
|
1.508
|
|
|
gamma1_hat
|
100
|
0
|
1.010
|
0.402
|
0.062
|
1.028
|
1.965
|
|
|
gamma2_hat
|
100
|
0
|
1.006
|
0.030
|
0.932
|
1.005
|
1.094
|
|
|
gamma3_hat
|
100
|
0
|
1.000
|
0.031
|
0.921
|
1.002
|
1.072
|
|
|
theta_hat
|
100
|
0
|
0.332
|
0.081
|
0.139
|
0.331
|
0.558
|
|
|
theta_hat_t_stats
|
100
|
0
|
4.518
|
0.972
|
1.945
|
4.632
|
6.625
|
|
|
R2_demand
|
100
|
0
|
0.366
|
0.031
|
0.286
|
0.368
|
0.439
|
|
|
R2_supply
|
100
|
0
|
0.356
|
0.037
|
0.250
|
0.356
|
0.453
|
|
\(\alpha_2 =
1.0\)
\(n = 50\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.881
|
0.911
|
7.719
|
9.780
|
12.297
|
|
|
alpha1_hat
|
100
|
0
|
0.820
|
3.832
|
−10.976
|
1.218
|
10.451
|
|
|
alpha2_hat
|
100
|
0
|
0.987
|
0.444
|
0.155
|
0.988
|
2.274
|
|
|
alpha3_hat
|
100
|
0
|
0.974
|
0.233
|
0.323
|
0.985
|
1.659
|
|
|
gamma0_hat
|
100
|
0
|
0.641
|
1.874
|
−6.248
|
0.962
|
3.918
|
|
|
gamma1_hat
|
100
|
0
|
−0.016
|
8.935
|
−31.752
|
0.069
|
59.196
|
|
|
gamma2_hat
|
100
|
0
|
1.053
|
0.269
|
0.550
|
1.019
|
1.986
|
|
|
gamma3_hat
|
100
|
0
|
1.061
|
0.272
|
0.609
|
1.016
|
2.385
|
|
|
theta_hat
|
100
|
0
|
0.545
|
0.970
|
−3.919
|
0.437
|
4.710
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.756
|
0.912
|
−2.111
|
0.817
|
2.723
|
|
|
R2_demand
|
100
|
0
|
0.433
|
0.229
|
−0.605
|
0.487
|
0.756
|
|
|
R2_supply
|
100
|
0
|
0.349
|
0.329
|
−1.560
|
0.432
|
0.740
|
|
\(n = 100\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.911
|
0.619
|
8.764
|
9.845
|
11.944
|
|
|
alpha1_hat
|
100
|
0
|
0.851
|
2.377
|
−4.596
|
0.806
|
6.231
|
|
|
alpha2_hat
|
100
|
0
|
0.991
|
0.288
|
0.353
|
0.978
|
1.800
|
|
|
alpha3_hat
|
100
|
0
|
0.999
|
0.152
|
0.641
|
0.992
|
1.480
|
|
|
gamma0_hat
|
100
|
0
|
0.931
|
0.933
|
−2.048
|
0.944
|
3.379
|
|
|
gamma1_hat
|
100
|
0
|
1.204
|
3.438
|
−6.497
|
1.582
|
9.392
|
|
|
gamma2_hat
|
100
|
0
|
1.011
|
0.142
|
0.694
|
0.998
|
1.433
|
|
|
gamma3_hat
|
100
|
0
|
0.996
|
0.146
|
0.687
|
0.990
|
1.483
|
|
|
theta_hat
|
100
|
0
|
0.333
|
0.356
|
−0.373
|
0.300
|
1.199
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.980
|
0.965
|
−0.936
|
0.981
|
3.298
|
|
|
R2_demand
|
100
|
0
|
0.402
|
0.166
|
−0.199
|
0.436
|
0.642
|
|
|
R2_supply
|
100
|
0
|
0.393
|
0.157
|
−0.309
|
0.416
|
0.675
|
|
\(n = 200\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.991
|
0.399
|
9.100
|
9.926
|
10.992
|
|
|
alpha1_hat
|
100
|
0
|
0.978
|
1.600
|
−2.596
|
1.086
|
4.918
|
|
|
alpha2_hat
|
100
|
0
|
1.004
|
0.184
|
0.606
|
0.988
|
1.468
|
|
|
alpha3_hat
|
100
|
0
|
0.998
|
0.087
|
0.807
|
0.986
|
1.228
|
|
|
gamma0_hat
|
100
|
0
|
1.030
|
0.696
|
−0.888
|
1.017
|
3.541
|
|
|
gamma1_hat
|
100
|
0
|
1.210
|
2.091
|
−6.672
|
1.261
|
6.603
|
|
|
gamma2_hat
|
100
|
0
|
0.990
|
0.104
|
0.637
|
0.987
|
1.256
|
|
|
gamma3_hat
|
100
|
0
|
0.998
|
0.100
|
0.708
|
0.998
|
1.296
|
|
|
theta_hat
|
100
|
0
|
0.311
|
0.221
|
−0.147
|
0.322
|
1.128
|
|
|
theta_hat_t_stats
|
100
|
0
|
1.407
|
0.889
|
−0.554
|
1.470
|
3.165
|
|
|
R2_demand
|
100
|
0
|
0.377
|
0.113
|
0.060
|
0.406
|
0.605
|
|
|
R2_supply
|
100
|
0
|
0.389
|
0.108
|
0.028
|
0.398
|
0.586
|
|
\(n = 1000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.009
|
0.199
|
9.552
|
10.022
|
10.515
|
|
|
alpha1_hat
|
100
|
0
|
1.064
|
0.807
|
−1.336
|
1.050
|
3.026
|
|
|
alpha2_hat
|
100
|
0
|
0.997
|
0.092
|
0.774
|
0.993
|
1.273
|
|
|
alpha3_hat
|
100
|
0
|
1.006
|
0.052
|
0.901
|
1.006
|
1.140
|
|
|
gamma0_hat
|
100
|
0
|
1.004
|
0.274
|
0.250
|
0.994
|
1.552
|
|
|
gamma1_hat
|
100
|
0
|
0.893
|
0.917
|
−1.210
|
0.904
|
2.858
|
|
|
gamma2_hat
|
100
|
0
|
0.999
|
0.039
|
0.931
|
0.992
|
1.100
|
|
|
gamma3_hat
|
100
|
0
|
1.004
|
0.042
|
0.910
|
1.003
|
1.102
|
|
|
theta_hat
|
100
|
0
|
0.339
|
0.102
|
0.130
|
0.340
|
0.599
|
|
|
theta_hat_t_stats
|
100
|
0
|
3.622
|
0.928
|
1.590
|
3.607
|
5.669
|
|
|
R2_demand
|
100
|
0
|
0.392
|
0.048
|
0.264
|
0.393
|
0.500
|
|
|
R2_supply
|
100
|
0
|
0.395
|
0.047
|
0.273
|
0.396
|
0.486
|
|
\(n = 2000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.983
|
0.130
|
9.671
|
9.990
|
10.252
|
|
|
alpha1_hat
|
100
|
0
|
1.070
|
0.629
|
−0.608
|
1.069
|
2.884
|
|
|
alpha2_hat
|
100
|
0
|
0.989
|
0.064
|
0.812
|
0.983
|
1.179
|
|
|
alpha3_hat
|
100
|
0
|
0.996
|
0.032
|
0.915
|
0.996
|
1.087
|
|
|
gamma0_hat
|
100
|
0
|
0.978
|
0.229
|
0.326
|
0.977
|
1.440
|
|
|
gamma1_hat
|
100
|
0
|
1.009
|
0.640
|
−0.480
|
1.067
|
2.528
|
|
|
gamma2_hat
|
100
|
0
|
1.002
|
0.034
|
0.939
|
1.000
|
1.092
|
|
|
gamma3_hat
|
100
|
0
|
1.002
|
0.038
|
0.935
|
0.997
|
1.104
|
|
|
theta_hat
|
100
|
0
|
0.335
|
0.065
|
0.178
|
0.330
|
0.476
|
|
|
theta_hat_t_stats
|
100
|
0
|
5.070
|
0.843
|
2.943
|
4.967
|
7.079
|
|
|
R2_demand
|
100
|
0
|
0.400
|
0.034
|
0.302
|
0.401
|
0.492
|
|
|
R2_supply
|
100
|
0
|
0.396
|
0.034
|
0.280
|
0.402
|
0.459
|
|
\(\alpha_2 =
5.0\)
\(n = 50\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.155
|
1.110
|
8.022
|
9.940
|
14.074
|
|
|
alpha1_hat
|
100
|
0
|
−0.743
|
17.362
|
−47.100
|
−1.777
|
52.841
|
|
|
alpha2_hat
|
100
|
0
|
5.352
|
1.980
|
0.878
|
5.258
|
10.056
|
|
|
alpha3_hat
|
100
|
0
|
1.028
|
0.251
|
0.492
|
0.996
|
2.140
|
|
|
gamma0_hat
|
100
|
0
|
0.539
|
2.743
|
−15.815
|
1.036
|
3.283
|
|
|
gamma1_hat
|
100
|
0
|
2.477
|
22.916
|
−105.349
|
3.018
|
69.242
|
|
|
gamma2_hat
|
100
|
0
|
1.036
|
0.375
|
0.531
|
0.967
|
3.254
|
|
|
gamma3_hat
|
100
|
0
|
1.076
|
0.435
|
0.566
|
1.011
|
4.192
|
|
|
theta_hat
|
100
|
0
|
0.424
|
0.697
|
−0.752
|
0.225
|
4.011
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.650
|
0.790
|
−1.640
|
0.623
|
2.371
|
|
|
R2_demand
|
100
|
0
|
0.344
|
0.381
|
−1.444
|
0.452
|
0.757
|
|
|
R2_supply
|
100
|
0
|
0.334
|
0.577
|
−3.722
|
0.456
|
0.785
|
|
\(n = 100\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.034
|
0.656
|
8.761
|
9.962
|
12.255
|
|
|
alpha1_hat
|
100
|
0
|
1.650
|
12.396
|
−33.550
|
0.718
|
38.354
|
|
|
alpha2_hat
|
100
|
0
|
4.988
|
1.422
|
2.300
|
4.944
|
9.145
|
|
|
alpha3_hat
|
100
|
0
|
1.001
|
0.156
|
0.577
|
1.020
|
1.546
|
|
|
gamma0_hat
|
100
|
0
|
0.989
|
1.015
|
−1.669
|
1.226
|
2.975
|
|
|
gamma1_hat
|
100
|
0
|
−1.129
|
15.342
|
−40.129
|
−0.687
|
35.773
|
|
|
gamma2_hat
|
100
|
0
|
1.015
|
0.161
|
0.705
|
1.003
|
1.458
|
|
|
gamma3_hat
|
100
|
0
|
0.982
|
0.136
|
0.668
|
0.976
|
1.400
|
|
|
theta_hat
|
100
|
0
|
0.368
|
0.330
|
−0.324
|
0.357
|
1.578
|
|
|
theta_hat_t_stats
|
100
|
0
|
1.177
|
0.895
|
−1.420
|
1.283
|
2.479
|
|
|
R2_demand
|
100
|
0
|
0.424
|
0.158
|
−0.076
|
0.453
|
0.721
|
|
|
R2_supply
|
100
|
0
|
0.453
|
0.129
|
0.009
|
0.462
|
0.678
|
|
\(n = 200\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.080
|
0.461
|
9.105
|
10.044
|
11.438
|
|
|
alpha1_hat
|
100
|
0
|
2.168
|
8.411
|
−18.957
|
2.191
|
21.653
|
|
|
alpha2_hat
|
100
|
0
|
4.968
|
0.909
|
2.360
|
4.973
|
7.329
|
|
|
alpha3_hat
|
100
|
0
|
1.003
|
0.094
|
0.807
|
0.992
|
1.269
|
|
|
gamma0_hat
|
100
|
0
|
0.991
|
0.655
|
−0.938
|
1.083
|
2.279
|
|
|
gamma1_hat
|
100
|
0
|
−1.505
|
9.800
|
−34.495
|
−1.450
|
22.510
|
|
|
gamma2_hat
|
100
|
0
|
0.996
|
0.101
|
0.776
|
0.982
|
1.237
|
|
|
gamma3_hat
|
100
|
0
|
1.000
|
0.100
|
0.813
|
0.998
|
1.248
|
|
|
theta_hat
|
100
|
0
|
0.381
|
0.241
|
−0.110
|
0.336
|
1.250
|
|
|
theta_hat_t_stats
|
100
|
0
|
1.849
|
0.899
|
−0.590
|
1.943
|
4.052
|
|
|
R2_demand
|
100
|
0
|
0.424
|
0.107
|
0.069
|
0.441
|
0.604
|
|
|
R2_supply
|
100
|
0
|
0.438
|
0.100
|
0.058
|
0.445
|
0.656
|
|
\(n = 1000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.017
|
0.207
|
9.502
|
10.010
|
10.834
|
|
|
alpha1_hat
|
100
|
0
|
1.106
|
3.724
|
−11.821
|
0.780
|
11.378
|
|
|
alpha2_hat
|
100
|
0
|
5.009
|
0.401
|
4.036
|
5.032
|
6.438
|
|
|
alpha3_hat
|
100
|
0
|
0.998
|
0.050
|
0.890
|
1.000
|
1.130
|
|
|
gamma0_hat
|
100
|
0
|
0.964
|
0.330
|
0.185
|
0.961
|
1.600
|
|
|
gamma1_hat
|
100
|
0
|
0.862
|
4.285
|
−10.247
|
1.234
|
9.269
|
|
|
gamma2_hat
|
100
|
0
|
1.004
|
0.052
|
0.881
|
0.999
|
1.128
|
|
|
gamma3_hat
|
100
|
0
|
1.000
|
0.045
|
0.885
|
1.000
|
1.095
|
|
|
theta_hat
|
100
|
0
|
0.338
|
0.095
|
0.096
|
0.328
|
0.580
|
|
|
theta_hat_t_stats
|
100
|
0
|
3.998
|
0.955
|
1.308
|
4.038
|
6.275
|
|
|
R2_demand
|
100
|
0
|
0.435
|
0.049
|
0.297
|
0.443
|
0.561
|
|
|
R2_supply
|
100
|
0
|
0.430
|
0.044
|
0.272
|
0.431
|
0.512
|
|
\(n = 2000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.998
|
0.146
|
9.661
|
10.001
|
10.377
|
|
|
alpha1_hat
|
100
|
0
|
0.880
|
2.928
|
−9.563
|
0.832
|
8.123
|
|
|
alpha2_hat
|
100
|
0
|
5.011
|
0.310
|
4.243
|
5.014
|
6.091
|
|
|
alpha3_hat
|
100
|
0
|
0.998
|
0.030
|
0.908
|
0.999
|
1.086
|
|
|
gamma0_hat
|
100
|
0
|
1.014
|
0.230
|
0.491
|
1.038
|
1.523
|
|
|
gamma1_hat
|
100
|
0
|
0.887
|
2.866
|
−7.982
|
0.992
|
7.093
|
|
|
gamma2_hat
|
100
|
0
|
0.999
|
0.034
|
0.902
|
1.004
|
1.083
|
|
|
gamma3_hat
|
100
|
0
|
0.999
|
0.032
|
0.934
|
0.995
|
1.096
|
|
|
theta_hat
|
100
|
0
|
0.330
|
0.069
|
0.186
|
0.322
|
0.474
|
|
|
theta_hat_t_stats
|
100
|
0
|
5.620
|
0.949
|
3.367
|
5.567
|
7.275
|
|
|
R2_demand
|
100
|
0
|
0.437
|
0.032
|
0.337
|
0.438
|
0.501
|
|
|
R2_supply
|
100
|
0
|
0.442
|
0.033
|
0.356
|
0.441
|
0.522
|
|
\(\alpha_2 =
20.0\)
\(n = 50\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.012
|
1.402
|
7.889
|
9.766
|
20.673
|
|
|
alpha1_hat
|
100
|
0
|
7.425
|
85.038
|
−130.833
|
7.690
|
601.521
|
|
|
alpha2_hat
|
100
|
0
|
19.400
|
7.157
|
3.583
|
18.262
|
41.696
|
|
|
alpha3_hat
|
100
|
0
|
1.006
|
0.267
|
0.477
|
0.984
|
2.735
|
|
|
gamma0_hat
|
100
|
0
|
0.855
|
1.443
|
−3.955
|
0.769
|
4.436
|
|
|
gamma1_hat
|
100
|
0
|
−27.478
|
100.281
|
−423.172
|
−8.324
|
164.203
|
|
|
gamma2_hat
|
100
|
0
|
1.021
|
0.218
|
0.473
|
1.035
|
1.712
|
|
|
gamma3_hat
|
100
|
0
|
1.045
|
0.215
|
0.485
|
1.019
|
1.618
|
|
|
theta_hat
|
100
|
0
|
0.507
|
0.610
|
−0.570
|
0.374
|
3.227
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.880
|
0.818
|
−1.123
|
0.917
|
2.508
|
|
|
R2_demand
|
100
|
0
|
0.371
|
0.875
|
−7.955
|
0.533
|
0.791
|
|
|
R2_supply
|
100
|
0
|
0.437
|
0.204
|
−0.273
|
0.474
|
0.745
|
|
\(n = 100\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.079
|
0.710
|
8.357
|
9.956
|
13.374
|
|
|
alpha1_hat
|
100
|
0
|
−5.827
|
50.208
|
−119.702
|
1.818
|
123.228
|
|
|
alpha2_hat
|
100
|
0
|
20.975
|
6.353
|
4.808
|
19.588
|
36.780
|
|
|
alpha3_hat
|
100
|
0
|
1.019
|
0.150
|
0.700
|
0.997
|
1.424
|
|
|
gamma0_hat
|
100
|
0
|
0.844
|
1.080
|
−2.479
|
0.841
|
2.832
|
|
|
gamma1_hat
|
100
|
0
|
−1.076
|
73.058
|
−309.002
|
5.744
|
216.125
|
|
|
gamma2_hat
|
100
|
0
|
1.035
|
0.164
|
0.622
|
1.004
|
1.578
|
|
|
gamma3_hat
|
100
|
0
|
1.001
|
0.159
|
0.653
|
0.989
|
1.507
|
|
|
theta_hat
|
100
|
0
|
0.370
|
0.455
|
−0.590
|
0.262
|
2.811
|
|
|
theta_hat_t_stats
|
100
|
0
|
1.149
|
0.941
|
−1.432
|
1.189
|
4.282
|
|
|
R2_demand
|
100
|
0
|
0.415
|
0.203
|
−0.875
|
0.450
|
0.720
|
|
|
R2_supply
|
100
|
0
|
0.441
|
0.141
|
0.018
|
0.456
|
0.709
|
|
\(n = 200\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.922
|
0.407
|
9.079
|
9.935
|
10.884
|
|
|
alpha1_hat
|
100
|
0
|
−1.508
|
28.924
|
−68.330
|
−3.907
|
68.355
|
|
|
alpha2_hat
|
100
|
0
|
19.881
|
3.396
|
11.564
|
19.740
|
28.292
|
|
|
alpha3_hat
|
100
|
0
|
0.982
|
0.101
|
0.768
|
0.984
|
1.289
|
|
|
gamma0_hat
|
100
|
0
|
0.963
|
0.740
|
−1.027
|
1.044
|
2.517
|
|
|
gamma1_hat
|
100
|
0
|
3.467
|
39.149
|
−95.363
|
5.773
|
124.265
|
|
|
gamma2_hat
|
100
|
0
|
1.001
|
0.107
|
0.722
|
0.993
|
1.323
|
|
|
gamma3_hat
|
100
|
0
|
1.007
|
0.115
|
0.692
|
1.011
|
1.284
|
|
|
theta_hat
|
100
|
0
|
0.335
|
0.224
|
−0.319
|
0.307
|
1.260
|
|
|
theta_hat_t_stats
|
100
|
0
|
1.666
|
0.957
|
−1.529
|
1.725
|
3.495
|
|
|
R2_demand
|
100
|
0
|
0.446
|
0.109
|
0.103
|
0.464
|
0.666
|
|
|
R2_supply
|
100
|
0
|
0.426
|
0.103
|
0.191
|
0.448
|
0.633
|
|
\(n = 1000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.014
|
0.213
|
9.553
|
10.005
|
10.726
|
|
|
alpha1_hat
|
100
|
0
|
−0.823
|
13.567
|
−28.407
|
−2.822
|
40.858
|
|
|
alpha2_hat
|
100
|
0
|
20.238
|
1.701
|
16.009
|
20.199
|
24.180
|
|
|
alpha3_hat
|
100
|
0
|
1.003
|
0.048
|
0.920
|
1.002
|
1.161
|
|
|
gamma0_hat
|
100
|
0
|
0.996
|
0.287
|
0.179
|
1.020
|
1.546
|
|
|
gamma1_hat
|
100
|
0
|
0.838
|
15.014
|
−52.139
|
2.099
|
33.161
|
|
|
gamma2_hat
|
100
|
0
|
1.000
|
0.046
|
0.914
|
1.001
|
1.111
|
|
|
gamma3_hat
|
100
|
0
|
1.009
|
0.043
|
0.914
|
1.004
|
1.135
|
|
|
theta_hat
|
100
|
0
|
0.332
|
0.085
|
0.141
|
0.328
|
0.651
|
|
|
theta_hat_t_stats
|
100
|
0
|
4.049
|
0.869
|
2.059
|
3.945
|
6.470
|
|
|
R2_demand
|
100
|
0
|
0.450
|
0.053
|
0.302
|
0.458
|
0.542
|
|
|
R2_supply
|
100
|
0
|
0.448
|
0.041
|
0.339
|
0.452
|
0.536
|
|
\(n = 2000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.988
|
0.137
|
9.717
|
9.973
|
10.406
|
|
|
alpha1_hat
|
100
|
0
|
1.148
|
10.368
|
−31.475
|
0.356
|
30.391
|
|
|
alpha2_hat
|
100
|
0
|
19.959
|
1.206
|
17.236
|
19.892
|
23.249
|
|
|
alpha3_hat
|
100
|
0
|
0.999
|
0.031
|
0.925
|
0.999
|
1.086
|
|
|
gamma0_hat
|
100
|
0
|
0.963
|
0.199
|
0.531
|
0.942
|
1.557
|
|
|
gamma1_hat
|
100
|
0
|
1.428
|
9.773
|
−22.716
|
1.421
|
22.038
|
|
|
gamma2_hat
|
100
|
0
|
1.004
|
0.028
|
0.907
|
1.002
|
1.069
|
|
|
gamma3_hat
|
100
|
0
|
1.001
|
0.033
|
0.920
|
1.001
|
1.070
|
|
|
theta_hat
|
100
|
0
|
0.334
|
0.057
|
0.212
|
0.335
|
0.480
|
|
|
theta_hat_t_stats
|
100
|
0
|
5.750
|
0.827
|
4.022
|
5.721
|
7.626
|
|
|
R2_demand
|
100
|
0
|
0.446
|
0.035
|
0.350
|
0.447
|
0.527
|
|
|
R2_supply
|
100
|
0
|
0.443
|
0.030
|
0.353
|
0.438
|
0.521
|
|
\(\theta =
0.5\)
\(\alpha_2 =
0.1\)
\(n = 50\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.068
|
1.045
|
7.915
|
9.982
|
13.936
|
|
|
alpha1_hat
|
100
|
0
|
1.002
|
1.373
|
−1.912
|
1.049
|
7.658
|
|
|
alpha2_hat
|
100
|
0
|
0.104
|
0.129
|
−0.276
|
0.093
|
0.585
|
|
|
alpha3_hat
|
100
|
0
|
0.987
|
0.208
|
0.523
|
0.976
|
1.566
|
|
|
gamma0_hat
|
100
|
0
|
0.738
|
2.124
|
−9.781
|
1.169
|
3.994
|
|
|
gamma1_hat
|
100
|
0
|
3.745
|
27.350
|
−15.803
|
1.268
|
265.584
|
|
|
gamma2_hat
|
100
|
0
|
1.013
|
0.253
|
0.454
|
0.956
|
1.860
|
|
|
gamma3_hat
|
100
|
0
|
1.032
|
0.233
|
0.498
|
1.021
|
1.832
|
|
|
theta_hat
|
100
|
0
|
−0.371
|
11.123
|
−104.077
|
0.420
|
13.239
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.380
|
1.033
|
−2.757
|
0.571
|
2.346
|
|
|
R2_demand
|
100
|
0
|
0.125
|
0.446
|
−2.641
|
0.237
|
0.556
|
|
|
R2_supply
|
100
|
0
|
0.054
|
0.956
|
−7.897
|
0.270
|
0.619
|
|
\(n = 100\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.942
|
0.620
|
8.837
|
9.822
|
12.284
|
|
|
alpha1_hat
|
100
|
0
|
1.077
|
0.863
|
−0.684
|
1.102
|
5.283
|
|
|
alpha2_hat
|
100
|
0
|
0.089
|
0.076
|
−0.161
|
0.093
|
0.261
|
|
|
alpha3_hat
|
100
|
0
|
0.994
|
0.148
|
0.680
|
0.990
|
1.396
|
|
|
gamma0_hat
|
100
|
0
|
0.998
|
1.121
|
−2.465
|
1.236
|
2.971
|
|
|
gamma1_hat
|
100
|
0
|
0.563
|
4.488
|
−26.166
|
0.846
|
17.330
|
|
|
gamma2_hat
|
100
|
0
|
0.996
|
0.170
|
0.620
|
1.001
|
1.466
|
|
|
gamma3_hat
|
100
|
0
|
1.008
|
0.139
|
0.745
|
1.000
|
1.398
|
|
|
theta_hat
|
100
|
0
|
0.757
|
2.486
|
−11.887
|
0.633
|
14.242
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.679
|
1.047
|
−2.177
|
0.649
|
3.384
|
|
|
R2_demand
|
100
|
0
|
0.200
|
0.209
|
−0.678
|
0.235
|
0.613
|
|
|
R2_supply
|
100
|
0
|
0.196
|
0.257
|
−0.857
|
0.265
|
0.540
|
|
\(n = 200\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.972
|
0.468
|
8.912
|
9.949
|
10.966
|
|
|
alpha1_hat
|
100
|
0
|
0.955
|
0.510
|
−0.215
|
0.908
|
2.705
|
|
|
alpha2_hat
|
100
|
0
|
0.102
|
0.050
|
−0.020
|
0.098
|
0.219
|
|
|
alpha3_hat
|
100
|
0
|
0.983
|
0.101
|
0.773
|
0.981
|
1.267
|
|
|
gamma0_hat
|
100
|
0
|
0.951
|
0.743
|
−2.020
|
1.069
|
2.575
|
|
|
gamma1_hat
|
100
|
0
|
0.952
|
2.608
|
−10.691
|
0.876
|
19.690
|
|
|
gamma2_hat
|
100
|
0
|
1.006
|
0.110
|
0.716
|
0.992
|
1.472
|
|
|
gamma3_hat
|
100
|
0
|
1.007
|
0.098
|
0.798
|
1.009
|
1.298
|
|
|
theta_hat
|
100
|
0
|
0.560
|
1.561
|
−10.086
|
0.565
|
9.036
|
|
|
theta_hat_t_stats
|
100
|
0
|
1.021
|
1.023
|
−2.788
|
1.057
|
3.733
|
|
|
R2_demand
|
100
|
0
|
0.188
|
0.151
|
−0.202
|
0.204
|
0.447
|
|
|
R2_supply
|
100
|
0
|
0.171
|
0.187
|
−0.831
|
0.196
|
0.525
|
|
\(n = 1000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.992
|
0.197
|
9.598
|
9.982
|
10.443
|
|
|
alpha1_hat
|
100
|
0
|
0.975
|
0.235
|
0.360
|
0.962
|
1.452
|
|
|
alpha2_hat
|
100
|
0
|
0.102
|
0.023
|
0.059
|
0.100
|
0.187
|
|
|
alpha3_hat
|
100
|
0
|
1.001
|
0.046
|
0.915
|
0.997
|
1.101
|
|
|
gamma0_hat
|
100
|
0
|
1.039
|
0.304
|
0.188
|
1.046
|
1.789
|
|
|
gamma1_hat
|
100
|
0
|
1.062
|
0.491
|
−0.258
|
1.052
|
2.196
|
|
|
gamma2_hat
|
100
|
0
|
0.997
|
0.045
|
0.897
|
0.998
|
1.134
|
|
|
gamma3_hat
|
100
|
0
|
0.993
|
0.049
|
0.880
|
0.995
|
1.139
|
|
|
theta_hat
|
100
|
0
|
0.462
|
0.262
|
−0.104
|
0.443
|
1.152
|
|
|
theta_hat_t_stats
|
100
|
0
|
2.045
|
1.003
|
−0.543
|
2.065
|
3.956
|
|
|
R2_demand
|
100
|
0
|
0.195
|
0.066
|
0.021
|
0.200
|
0.320
|
|
|
R2_supply
|
100
|
0
|
0.209
|
0.054
|
0.063
|
0.215
|
0.345
|
|
\(n = 2000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.008
|
0.139
|
9.666
|
10.013
|
10.278
|
|
|
alpha1_hat
|
100
|
0
|
0.995
|
0.176
|
0.583
|
0.985
|
1.451
|
|
|
alpha2_hat
|
100
|
0
|
0.101
|
0.017
|
0.064
|
0.102
|
0.144
|
|
|
alpha3_hat
|
100
|
0
|
1.005
|
0.030
|
0.930
|
1.005
|
1.080
|
|
|
gamma0_hat
|
100
|
0
|
0.971
|
0.218
|
0.494
|
0.981
|
1.460
|
|
|
gamma1_hat
|
100
|
0
|
0.942
|
0.341
|
−0.036
|
0.998
|
1.505
|
|
|
gamma2_hat
|
100
|
0
|
1.004
|
0.034
|
0.932
|
1.003
|
1.078
|
|
|
gamma3_hat
|
100
|
0
|
1.001
|
0.031
|
0.933
|
1.000
|
1.105
|
|
|
theta_hat
|
100
|
0
|
0.533
|
0.171
|
0.211
|
0.507
|
0.969
|
|
|
theta_hat_t_stats
|
100
|
0
|
3.396
|
0.832
|
1.488
|
3.371
|
5.278
|
|
|
R2_demand
|
100
|
0
|
0.202
|
0.041
|
0.083
|
0.205
|
0.277
|
|
|
R2_supply
|
100
|
0
|
0.200
|
0.039
|
0.106
|
0.202
|
0.287
|
|
\(\alpha_2 =
0.5\)
\(n = 50\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.918
|
1.030
|
7.960
|
9.700
|
14.079
|
|
|
alpha1_hat
|
100
|
0
|
0.635
|
2.503
|
−4.577
|
0.383
|
7.811
|
|
|
alpha2_hat
|
100
|
0
|
0.522
|
0.295
|
−0.166
|
0.537
|
1.309
|
|
|
alpha3_hat
|
100
|
0
|
0.993
|
0.217
|
0.623
|
0.971
|
1.780
|
|
|
gamma0_hat
|
100
|
0
|
0.330
|
1.867
|
−7.538
|
0.554
|
3.598
|
|
|
gamma1_hat
|
100
|
0
|
−3.952
|
43.802
|
−412.503
|
1.299
|
40.828
|
|
|
gamma2_hat
|
100
|
0
|
1.066
|
0.258
|
0.526
|
1.025
|
1.782
|
|
|
gamma3_hat
|
100
|
0
|
1.056
|
0.285
|
0.593
|
0.997
|
2.381
|
|
|
theta_hat
|
100
|
0
|
1.763
|
9.830
|
−6.911
|
0.527
|
95.646
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.822
|
0.981
|
−2.637
|
0.863
|
3.001
|
|
|
R2_demand
|
100
|
0
|
0.262
|
0.375
|
−1.820
|
0.348
|
0.696
|
|
|
R2_supply
|
100
|
0
|
0.151
|
0.427
|
−2.232
|
0.243
|
0.654
|
|
\(n = 100\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.042
|
0.710
|
8.658
|
9.920
|
12.798
|
|
|
alpha1_hat
|
100
|
0
|
1.142
|
1.940
|
−3.704
|
0.923
|
7.108
|
|
|
alpha2_hat
|
100
|
0
|
0.494
|
0.197
|
−0.054
|
0.486
|
1.028
|
|
|
alpha3_hat
|
100
|
0
|
1.019
|
0.154
|
0.644
|
1.032
|
1.481
|
|
|
gamma0_hat
|
100
|
0
|
1.102
|
1.004
|
−1.346
|
1.185
|
3.312
|
|
|
gamma1_hat
|
100
|
0
|
0.687
|
6.103
|
−21.565
|
1.301
|
41.843
|
|
|
gamma2_hat
|
100
|
0
|
0.993
|
0.147
|
0.644
|
0.981
|
1.395
|
|
|
gamma3_hat
|
100
|
0
|
0.989
|
0.140
|
0.699
|
1.000
|
1.514
|
|
|
theta_hat
|
100
|
0
|
0.549
|
1.016
|
−5.737
|
0.387
|
3.951
|
|
|
theta_hat_t_stats
|
100
|
0
|
1.127
|
0.960
|
−1.718
|
1.152
|
2.974
|
|
|
R2_demand
|
100
|
0
|
0.260
|
0.243
|
−1.117
|
0.336
|
0.554
|
|
|
R2_supply
|
100
|
0
|
0.297
|
0.186
|
−0.250
|
0.326
|
0.590
|
|
\(n = 200\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.008
|
0.452
|
9.236
|
9.951
|
11.002
|
|
|
alpha1_hat
|
100
|
0
|
0.901
|
1.288
|
−2.563
|
0.945
|
4.009
|
|
|
alpha2_hat
|
100
|
0
|
0.511
|
0.126
|
0.169
|
0.517
|
0.786
|
|
|
alpha3_hat
|
100
|
0
|
0.992
|
0.093
|
0.735
|
0.992
|
1.356
|
|
|
gamma0_hat
|
100
|
0
|
1.006
|
0.654
|
−0.650
|
0.996
|
2.533
|
|
|
gamma1_hat
|
100
|
0
|
0.888
|
1.891
|
−8.429
|
0.982
|
6.502
|
|
|
gamma2_hat
|
100
|
0
|
0.997
|
0.101
|
0.789
|
0.992
|
1.328
|
|
|
gamma3_hat
|
100
|
0
|
0.993
|
0.107
|
0.778
|
0.981
|
1.295
|
|
|
theta_hat
|
100
|
0
|
0.526
|
0.355
|
−0.233
|
0.480
|
2.127
|
|
|
theta_hat_t_stats
|
100
|
0
|
1.860
|
0.876
|
−0.426
|
1.991
|
3.695
|
|
|
R2_demand
|
100
|
0
|
0.270
|
0.137
|
−0.168
|
0.277
|
0.526
|
|
|
R2_supply
|
100
|
0
|
0.275
|
0.112
|
−0.067
|
0.288
|
0.537
|
|
\(n = 1000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.985
|
0.190
|
9.511
|
9.980
|
10.607
|
|
|
alpha1_hat
|
100
|
0
|
1.057
|
0.577
|
−0.562
|
1.106
|
2.106
|
|
|
alpha2_hat
|
100
|
0
|
0.492
|
0.063
|
0.370
|
0.482
|
0.652
|
|
|
alpha3_hat
|
100
|
0
|
0.997
|
0.045
|
0.884
|
0.996
|
1.102
|
|
|
gamma0_hat
|
100
|
0
|
0.982
|
0.338
|
−0.035
|
1.001
|
2.124
|
|
|
gamma1_hat
|
100
|
0
|
0.902
|
0.769
|
−0.901
|
0.913
|
2.540
|
|
|
gamma2_hat
|
100
|
0
|
1.001
|
0.050
|
0.801
|
1.000
|
1.140
|
|
|
gamma3_hat
|
100
|
0
|
1.003
|
0.046
|
0.873
|
0.999
|
1.142
|
|
|
theta_hat
|
100
|
0
|
0.524
|
0.125
|
0.268
|
0.531
|
0.880
|
|
|
theta_hat_t_stats
|
100
|
0
|
4.388
|
0.892
|
2.378
|
4.412
|
6.896
|
|
|
R2_demand
|
100
|
0
|
0.292
|
0.056
|
0.164
|
0.300
|
0.415
|
|
|
R2_supply
|
100
|
0
|
0.285
|
0.055
|
0.079
|
0.284
|
0.403
|
|
\(n = 2000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.997
|
0.154
|
9.672
|
9.988
|
10.373
|
|
|
alpha1_hat
|
100
|
0
|
0.951
|
0.370
|
0.116
|
0.988
|
2.276
|
|
|
alpha2_hat
|
100
|
0
|
0.505
|
0.040
|
0.409
|
0.505
|
0.618
|
|
|
alpha3_hat
|
100
|
0
|
1.001
|
0.034
|
0.914
|
0.997
|
1.070
|
|
|
gamma0_hat
|
100
|
0
|
0.964
|
0.232
|
0.407
|
0.968
|
1.403
|
|
|
gamma1_hat
|
100
|
0
|
1.000
|
0.510
|
−0.121
|
0.996
|
2.040
|
|
|
gamma2_hat
|
100
|
0
|
1.005
|
0.035
|
0.936
|
1.008
|
1.084
|
|
|
gamma3_hat
|
100
|
0
|
1.004
|
0.036
|
0.907
|
1.003
|
1.092
|
|
|
theta_hat
|
100
|
0
|
0.507
|
0.091
|
0.315
|
0.521
|
0.694
|
|
|
theta_hat_t_stats
|
100
|
0
|
6.240
|
0.928
|
4.305
|
6.243
|
8.591
|
|
|
R2_demand
|
100
|
0
|
0.286
|
0.046
|
0.149
|
0.289
|
0.386
|
|
|
R2_supply
|
100
|
0
|
0.283
|
0.037
|
0.175
|
0.283
|
0.361
|
|
\(\alpha_2 =
1.0\)
\(n = 50\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.025
|
1.054
|
8.416
|
9.819
|
13.799
|
|
|
alpha1_hat
|
100
|
0
|
1.174
|
4.966
|
−12.688
|
0.825
|
25.156
|
|
|
alpha2_hat
|
100
|
0
|
0.989
|
0.588
|
−0.632
|
0.949
|
2.952
|
|
|
alpha3_hat
|
100
|
0
|
1.004
|
0.258
|
0.489
|
0.952
|
1.923
|
|
|
gamma0_hat
|
100
|
0
|
0.814
|
1.716
|
−9.207
|
0.869
|
4.640
|
|
|
gamma1_hat
|
100
|
0
|
−3.798
|
28.528
|
−259.759
|
2.076
|
17.332
|
|
|
gamma2_hat
|
100
|
0
|
1.034
|
0.225
|
0.592
|
1.059
|
2.011
|
|
|
gamma3_hat
|
100
|
0
|
1.009
|
0.230
|
0.473
|
1.016
|
1.900
|
|
|
theta_hat
|
100
|
0
|
1.090
|
3.228
|
−1.121
|
0.344
|
30.113
|
|
|
theta_hat_t_stats
|
100
|
0
|
0.864
|
0.940
|
−1.943
|
0.946
|
3.401
|
|
|
R2_demand
|
100
|
0
|
0.275
|
0.424
|
−2.122
|
0.397
|
0.744
|
|
|
R2_supply
|
100
|
0
|
0.306
|
0.345
|
−2.229
|
0.362
|
0.736
|
|
\(n = 100\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.014
|
0.683
|
8.583
|
9.864
|
12.234
|
|
|
alpha1_hat
|
100
|
0
|
0.899
|
2.964
|
−7.428
|
0.718
|
8.488
|
|
|
alpha2_hat
|
100
|
0
|
1.017
|
0.314
|
0.322
|
1.005
|
2.141
|
|
|
alpha3_hat
|
100
|
0
|
0.993
|
0.136
|
0.714
|
0.979
|
1.387
|
|
|
gamma0_hat
|
100
|
0
|
0.880
|
0.947
|
−2.870
|
0.853
|
2.937
|
|
|
gamma1_hat
|
100
|
0
|
0.723
|
4.365
|
−14.154
|
1.815
|
9.577
|
|
|
gamma2_hat
|
100
|
0
|
1.019
|
0.142
|
0.696
|
1.016
|
1.576
|
|
|
gamma3_hat
|
100
|
0
|
1.008
|
0.136
|
0.677
|
0.994
|
1.416
|
|
|
theta_hat
|
100
|
0
|
0.542
|
0.431
|
−0.306
|
0.429
|
2.409
|
|
|
theta_hat_t_stats
|
100
|
0
|
1.448
|
0.846
|
−0.844
|
1.372
|
3.426
|
|
|
R2_demand
|
100
|
0
|
0.304
|
0.191
|
−0.249
|
0.329
|
0.608
|
|
|
R2_supply
|
100
|
0
|
0.329
|
0.162
|
−0.256
|
0.362
|
0.623
|
|
\(n = 200\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.052
|
0.488
|
8.847
|
10.022
|
11.306
|
|
|
alpha1_hat
|
100
|
0
|
1.198
|
2.177
|
−3.931
|
1.367
|
6.972
|
|
|
alpha2_hat
|
100
|
0
|
0.993
|
0.241
|
0.512
|
0.976
|
1.761
|
|
|
alpha3_hat
|
100
|
0
|
1.016
|
0.106
|
0.780
|
1.002
|
1.317
|
|
|
gamma0_hat
|
100
|
0
|
0.862
|
0.718
|
−2.439
|
0.947
|
2.256
|
|
|
gamma1_hat
|
100
|
0
|
0.604
|
2.878
|
−7.175
|
1.118
|
6.459
|
|
|
gamma2_hat
|
100
|
0
|
1.011
|
0.102
|
0.800
|
0.993
|
1.481
|
|
|
gamma3_hat
|
100
|
0
|
1.015
|
0.098
|
0.820
|
0.999
|
1.366
|
|
|
theta_hat
|
100
|
0
|
0.571
|
0.309
|
−0.035
|
0.516
|
1.487
|
|
|
theta_hat_t_stats
|
100
|
0
|
2.176
|
0.873
|
−0.160
|
2.116
|
4.171
|
|
|
R2_demand
|
100
|
0
|
0.293
|
0.138
|
−0.167
|
0.305
|
0.528
|
|
|
R2_supply
|
100
|
0
|
0.294
|
0.156
|
−0.291
|
0.313
|
0.585
|
|
\(n = 1000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.032
|
0.204
|
9.599
|
10.041
|
10.669
|
|
|
alpha1_hat
|
100
|
0
|
1.042
|
0.942
|
−1.293
|
1.059
|
3.488
|
|
|
alpha2_hat
|
100
|
0
|
1.005
|
0.111
|
0.657
|
1.021
|
1.303
|
|
|
alpha3_hat
|
100
|
0
|
1.004
|
0.041
|
0.910
|
1.006
|
1.118
|
|
|
gamma0_hat
|
100
|
0
|
0.930
|
0.343
|
0.017
|
0.994
|
1.878
|
|
|
gamma1_hat
|
100
|
0
|
1.012
|
1.121
|
−1.948
|
1.030
|
4.781
|
|
|
gamma2_hat
|
100
|
0
|
1.006
|
0.052
|
0.900
|
0.999
|
1.138
|
|
|
gamma3_hat
|
100
|
0
|
1.007
|
0.041
|
0.875
|
1.007
|
1.106
|
|
|
theta_hat
|
100
|
0
|
0.510
|
0.120
|
0.157
|
0.505
|
0.916
|
|
|
theta_hat_t_stats
|
100
|
0
|
4.850
|
0.867
|
1.761
|
4.874
|
6.715
|
|
|
R2_demand
|
100
|
0
|
0.313
|
0.053
|
0.145
|
0.312
|
0.413
|
|
|
R2_supply
|
100
|
0
|
0.301
|
0.061
|
0.114
|
0.305
|
0.434
|
|
\(n = 2000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.032
|
0.154
|
9.640
|
10.025
|
10.500
|
|
|
alpha1_hat
|
100
|
0
|
1.070
|
0.659
|
−0.595
|
0.976
|
2.432
|
|
|
alpha2_hat
|
100
|
0
|
1.003
|
0.079
|
0.770
|
1.007
|
1.191
|
|
|
alpha3_hat
|
100
|
0
|
1.005
|
0.031
|
0.933
|
1.000
|
1.081
|
|
|
gamma0_hat
|
100
|
0
|
0.959
|
0.243
|
0.362
|
0.964
|
1.572
|
|
|
gamma1_hat
|
100
|
0
|
1.038
|
0.850
|
−1.009
|
1.011
|
3.044
|
|
|
gamma2_hat
|
100
|
0
|
1.008
|
0.034
|
0.924
|
1.006
|
1.079
|
|
|
gamma3_hat
|
100
|
0
|
1.004
|
0.031
|
0.916
|
1.004
|
1.088
|
|
|
theta_hat
|
100
|
0
|
0.498
|
0.081
|
0.262
|
0.494
|
0.674
|
|
|
theta_hat_t_stats
|
100
|
0
|
6.805
|
0.913
|
4.385
|
6.800
|
9.071
|
|
|
R2_demand
|
100
|
0
|
0.313
|
0.042
|
0.214
|
0.318
|
0.400
|
|
|
R2_supply
|
100
|
0
|
0.318
|
0.041
|
0.226
|
0.317
|
0.417
|
|
\(\alpha_2 =
5.0\)
\(n = 50\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.905
|
0.857
|
7.903
|
9.839
|
13.046
|
|
|
alpha1_hat
|
100
|
0
|
1.229
|
19.905
|
−56.477
|
−1.308
|
46.467
|
|
|
alpha2_hat
|
100
|
0
|
4.838
|
2.291
|
−0.843
|
5.057
|
11.967
|
|
|
alpha3_hat
|
100
|
0
|
0.994
|
0.178
|
0.653
|
0.978
|
1.503
|
|
|
gamma0_hat
|
100
|
0
|
0.737
|
1.491
|
−4.036
|
1.038
|
3.492
|
|
|
gamma1_hat
|
100
|
0
|
−5.312
|
160.588
|
−817.729
|
−0.157
|
1227.512
|
|
|
gamma2_hat
|
100
|
0
|
1.031
|
0.235
|
0.594
|
0.993
|
1.703
|
|
|
gamma3_hat
|
100
|
0
|
1.046
|
0.223
|
0.616
|
1.027
|
1.849
|
|
|
theta_hat
|
100
|
0
|
0.649
|
4.575
|
−36.293
|
0.580
|
20.544
|
|
|
theta_hat_t_stats
|
100
|
0
|
1.087
|
0.931
|
−2.335
|
1.315
|
2.911
|
|
|
R2_demand
|
100
|
0
|
0.355
|
0.287
|
−1.042
|
0.408
|
0.736
|
|
|
R2_supply
|
100
|
0
|
0.350
|
0.223
|
−0.321
|
0.408
|
0.743
|
|
\(n = 100\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.060
|
0.675
|
8.425
|
10.004
|
12.044
|
|
|
alpha1_hat
|
100
|
0
|
0.282
|
13.587
|
−33.200
|
−1.095
|
43.051
|
|
|
alpha2_hat
|
100
|
0
|
5.147
|
1.474
|
0.676
|
5.129
|
9.030
|
|
|
alpha3_hat
|
100
|
0
|
0.999
|
0.156
|
0.745
|
0.993
|
1.553
|
|
|
gamma0_hat
|
100
|
0
|
0.844
|
1.140
|
−2.899
|
1.024
|
2.943
|
|
|
gamma1_hat
|
100
|
0
|
0.865
|
26.412
|
−216.314
|
3.537
|
34.904
|
|
|
gamma2_hat
|
100
|
0
|
1.012
|
0.164
|
0.663
|
0.998
|
1.461
|
|
|
gamma3_hat
|
100
|
0
|
1.014
|
0.162
|
0.692
|
1.028
|
1.501
|
|
|
theta_hat
|
100
|
0
|
0.549
|
0.553
|
−0.152
|
0.444
|
4.770
|
|
|
theta_hat_t_stats
|
100
|
0
|
1.443
|
0.743
|
−0.614
|
1.499
|
2.981
|
|
|
R2_demand
|
100
|
0
|
0.312
|
0.260
|
−0.988
|
0.370
|
0.586
|
|
|
R2_supply
|
100
|
0
|
0.293
|
0.237
|
−1.082
|
0.342
|
0.601
|
|
\(n = 200\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.960
|
0.473
|
8.789
|
9.966
|
11.243
|
|
|
alpha1_hat
|
100
|
0
|
−0.095
|
9.647
|
−19.686
|
0.279
|
20.684
|
|
|
alpha2_hat
|
100
|
0
|
5.058
|
1.106
|
2.841
|
4.852
|
8.631
|
|
|
alpha3_hat
|
100
|
0
|
0.994
|
0.114
|
0.770
|
0.985
|
1.251
|
|
|
gamma0_hat
|
100
|
0
|
0.880
|
0.783
|
−2.403
|
0.970
|
2.485
|
|
|
gamma1_hat
|
100
|
0
|
0.108
|
12.032
|
−39.482
|
0.970
|
26.673
|
|
|
gamma2_hat
|
100
|
0
|
1.010
|
0.117
|
0.754
|
1.012
|
1.428
|
|
|
gamma3_hat
|
100
|
0
|
1.014
|
0.124
|
0.776
|
0.992
|
1.414
|
|
|
theta_hat
|
100
|
0
|
0.552
|
0.268
|
−0.004
|
0.518
|
1.557
|
|
|
theta_hat_t_stats
|
100
|
0
|
2.441
|
0.876
|
−0.022
|
2.376
|
4.325
|
|
|
R2_demand
|
100
|
0
|
0.342
|
0.130
|
−0.090
|
0.361
|
0.561
|
|
|
R2_supply
|
100
|
0
|
0.324
|
0.141
|
−0.306
|
0.333
|
0.580
|
|
\(n = 1000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.016
|
0.184
|
9.555
|
10.003
|
10.435
|
|
|
alpha1_hat
|
100
|
0
|
1.571
|
3.895
|
−7.121
|
1.534
|
10.478
|
|
|
alpha2_hat
|
100
|
0
|
4.965
|
0.453
|
3.772
|
4.948
|
5.792
|
|
|
alpha3_hat
|
100
|
0
|
1.003
|
0.043
|
0.913
|
1.002
|
1.110
|
|
|
gamma0_hat
|
100
|
0
|
1.013
|
0.281
|
0.181
|
0.998
|
1.616
|
|
|
gamma1_hat
|
100
|
0
|
0.285
|
4.807
|
−9.959
|
0.197
|
11.288
|
|
|
gamma2_hat
|
100
|
0
|
0.999
|
0.040
|
0.905
|
1.003
|
1.133
|
|
|
gamma3_hat
|
100
|
0
|
0.994
|
0.044
|
0.886
|
0.990
|
1.122
|
|
|
theta_hat
|
100
|
0
|
0.511
|
0.099
|
0.243
|
0.515
|
0.698
|
|
|
theta_hat_t_stats
|
100
|
0
|
5.378
|
0.876
|
3.201
|
5.441
|
7.254
|
|
|
R2_demand
|
100
|
0
|
0.341
|
0.053
|
0.182
|
0.347
|
0.431
|
|
|
R2_supply
|
100
|
0
|
0.353
|
0.050
|
0.219
|
0.361
|
0.474
|
|
\(n = 2000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.005
|
0.139
|
9.680
|
10.007
|
10.451
|
|
|
alpha1_hat
|
100
|
0
|
1.166
|
2.547
|
−3.731
|
0.902
|
6.745
|
|
|
alpha2_hat
|
100
|
0
|
4.994
|
0.341
|
4.223
|
5.031
|
5.811
|
|
|
alpha3_hat
|
100
|
0
|
1.004
|
0.034
|
0.927
|
1.005
|
1.089
|
|
|
gamma0_hat
|
100
|
0
|
1.003
|
0.201
|
0.508
|
1.017
|
1.605
|
|
|
gamma1_hat
|
100
|
0
|
0.523
|
3.522
|
−11.355
|
0.797
|
9.824
|
|
|
gamma2_hat
|
100
|
0
|
0.999
|
0.028
|
0.905
|
0.997
|
1.072
|
|
|
gamma3_hat
|
100
|
0
|
0.998
|
0.029
|
0.883
|
1.000
|
1.047
|
|
|
theta_hat
|
100
|
0
|
0.509
|
0.084
|
0.293
|
0.506
|
0.722
|
|
|
theta_hat_t_stats
|
100
|
0
|
7.599
|
0.987
|
4.524
|
7.715
|
10.192
|
|
|
R2_demand
|
100
|
0
|
0.344
|
0.042
|
0.237
|
0.346
|
0.452
|
|
|
R2_supply
|
100
|
0
|
0.345
|
0.034
|
0.254
|
0.345
|
0.406
|
|
\(\alpha_2 =
20.0\)
\(n = 50\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.952
|
1.012
|
8.115
|
9.864
|
13.583
|
|
|
alpha1_hat
|
100
|
0
|
−6.081
|
81.140
|
−175.858
|
−5.806
|
224.524
|
|
|
alpha2_hat
|
100
|
0
|
20.447
|
8.570
|
−2.178
|
20.765
|
39.275
|
|
|
alpha3_hat
|
100
|
0
|
0.966
|
0.235
|
0.550
|
0.939
|
1.762
|
|
|
gamma0_hat
|
100
|
0
|
0.839
|
1.760
|
−7.683
|
1.029
|
4.745
|
|
|
gamma1_hat
|
100
|
0
|
−209.454
|
1634.353
|
−16118.530
|
−2.292
|
213.426
|
|
|
gamma2_hat
|
100
|
0
|
1.024
|
0.252
|
0.573
|
1.000
|
2.014
|
|
|
gamma3_hat
|
100
|
0
|
1.041
|
0.246
|
0.507
|
1.020
|
1.782
|
|
|
theta_hat
|
100
|
0
|
1.795
|
9.343
|
−0.650
|
0.528
|
92.086
|
|
|
theta_hat_t_stats
|
100
|
0
|
1.147
|
0.959
|
−1.824
|
1.186
|
3.131
|
|
|
R2_demand
|
100
|
0
|
0.319
|
0.389
|
−1.852
|
0.434
|
0.806
|
|
|
R2_supply
|
100
|
0
|
0.316
|
0.432
|
−2.774
|
0.401
|
0.748
|
|
\(n = 100\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.919
|
0.624
|
8.551
|
9.892
|
12.815
|
|
|
alpha1_hat
|
100
|
0
|
3.180
|
50.544
|
−105.249
|
3.688
|
130.740
|
|
|
alpha2_hat
|
100
|
0
|
19.360
|
6.359
|
5.189
|
18.479
|
43.643
|
|
|
alpha3_hat
|
100
|
0
|
1.000
|
0.152
|
0.649
|
0.982
|
1.449
|
|
|
gamma0_hat
|
100
|
0
|
1.025
|
0.794
|
−0.906
|
1.065
|
3.289
|
|
|
gamma1_hat
|
100
|
0
|
−13.671
|
68.100
|
−233.919
|
−0.987
|
132.235
|
|
|
gamma2_hat
|
100
|
0
|
1.000
|
0.125
|
0.665
|
0.995
|
1.288
|
|
|
gamma3_hat
|
100
|
0
|
0.995
|
0.142
|
0.656
|
0.976
|
1.316
|
|
|
theta_hat
|
100
|
0
|
0.599
|
0.411
|
−0.114
|
0.550
|
2.040
|
|
|
theta_hat_t_stats
|
100
|
0
|
1.672
|
0.864
|
−0.411
|
1.635
|
3.555
|
|
|
R2_demand
|
100
|
0
|
0.351
|
0.274
|
−1.872
|
0.380
|
0.676
|
|
|
R2_supply
|
100
|
0
|
0.356
|
0.144
|
−0.077
|
0.350
|
0.668
|
|
\(n = 200\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
10.013
|
0.473
|
8.633
|
9.987
|
11.164
|
|
|
alpha1_hat
|
100
|
0
|
0.905
|
38.348
|
−127.127
|
7.208
|
71.531
|
|
|
alpha2_hat
|
100
|
0
|
20.126
|
4.806
|
9.769
|
19.467
|
38.683
|
|
|
alpha3_hat
|
100
|
0
|
1.013
|
0.100
|
0.800
|
1.018
|
1.314
|
|
|
gamma0_hat
|
100
|
0
|
0.966
|
0.730
|
−2.368
|
1.007
|
2.269
|
|
|
gamma1_hat
|
100
|
0
|
−5.638
|
39.944
|
−115.338
|
0.932
|
78.109
|
|
|
gamma2_hat
|
100
|
0
|
0.995
|
0.109
|
0.738
|
0.993
|
1.296
|
|
|
gamma3_hat
|
100
|
0
|
1.007
|
0.112
|
0.767
|
1.010
|
1.450
|
|
|
theta_hat
|
100
|
0
|
0.557
|
0.275
|
0.022
|
0.550
|
1.717
|
|
|
theta_hat_t_stats
|
100
|
0
|
2.454
|
0.875
|
0.119
|
2.507
|
4.810
|
|
|
R2_demand
|
100
|
0
|
0.326
|
0.140
|
−0.064
|
0.359
|
0.547
|
|
|
R2_supply
|
100
|
0
|
0.346
|
0.124
|
−0.145
|
0.363
|
0.584
|
|
\(n = 1000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.992
|
0.192
|
9.555
|
9.974
|
10.513
|
|
|
alpha1_hat
|
100
|
0
|
2.092
|
14.772
|
−39.193
|
3.266
|
45.123
|
|
|
alpha2_hat
|
100
|
0
|
19.835
|
1.710
|
14.689
|
19.769
|
23.925
|
|
|
alpha3_hat
|
100
|
0
|
1.002
|
0.042
|
0.916
|
0.996
|
1.100
|
|
|
gamma0_hat
|
100
|
0
|
1.012
|
0.291
|
0.075
|
0.997
|
1.996
|
|
|
gamma1_hat
|
100
|
0
|
2.384
|
16.937
|
−40.210
|
2.903
|
41.254
|
|
|
gamma2_hat
|
100
|
0
|
0.997
|
0.044
|
0.879
|
1.000
|
1.134
|
|
|
gamma3_hat
|
100
|
0
|
1.004
|
0.048
|
0.911
|
1.003
|
1.147
|
|
|
theta_hat
|
100
|
0
|
0.494
|
0.096
|
0.264
|
0.503
|
0.706
|
|
|
theta_hat_t_stats
|
100
|
0
|
5.299
|
0.847
|
3.097
|
5.434
|
7.016
|
|
|
R2_demand
|
100
|
0
|
0.356
|
0.048
|
0.230
|
0.362
|
0.464
|
|
|
R2_supply
|
100
|
0
|
0.357
|
0.042
|
0.248
|
0.358
|
0.449
|
|
\(n = 2000\)
|
|
Unique (#)
|
Missing (%)
|
Mean
|
SD
|
Min
|
Median
|
Max
|
|
|
group_id_k
|
100
|
0
|
50.500
|
29.011
|
1.000
|
50.500
|
100.000
|
|
|
alpha0_hat
|
100
|
0
|
9.992
|
0.192
|
9.555
|
9.974
|
10.513
|
|
|
alpha1_hat
|
100
|
0
|
2.092
|
14.772
|
−39.193
|
3.266
|
45.123
|
|
|
alpha2_hat
|
100
|
0
|
19.835
|
1.710
|
14.689
|
19.769
|
23.925
|
|
|
alpha3_hat
|
100
|
0
|
1.002
|
0.042
|
0.916
|
0.996
|
1.100
|
|
|
gamma0_hat
|
100
|
0
|
1.012
|
0.291
|
0.075
|
0.997
|
1.996
|
|
|
gamma1_hat
|
100
|
0
|
2.384
|
16.937
|
−40.210
|
2.903
|
41.254
|
|
|
gamma2_hat
|
100
|
0
|
0.997
|
0.044
|
0.879
|
1.000
|
1.134
|
|
|
gamma3_hat
|
100
|
0
|
1.004
|
0.048
|
0.911
|
1.003
|
1.147
|
|
|
theta_hat
|
100
|
0
|
0.494
|
0.096
|
0.264
|
0.503
|
0.706
|
|
|
theta_hat_t_stats
|
100
|
0
|
5.299
|
0.847
|
3.097
|
5.434
|
7.016
|
|
|
R2_demand
|
100
|
0
|
0.356
|
0.048
|
0.230
|
0.362
|
0.464
|
|
|
R2_supply
|
100
|
0
|
0.357
|
0.042
|
0.248
|
0.358
|
0.449
|
|